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8:00 p.m.
Donald Trump says he's now "totally committed to the Republican party" and won't run as an independent if he's not the GOP nominee.
Trump is responding to concerns that he would stay in the race as an independent if another Republican wins the nomination, and send Hillary Clinton to the White House by splitting the conservative vote.
The business mogul says he's gained great respect for the people he's met during his candidacy and is honored to be the front-runner.
He says he'd "do everything in my power to beat Hillary Clinton."
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7: 58 p.m.
Noticed a growing rivalry between Donald Trump and Ted Cruz? They say there's nothing to see here.
Asked about recent statements they've made on the 2016 campaign trail, Trump and Cruz both played nice on the Republican debate stage Tuesday night.
Trump says Cruz has a "wonderful temperament" and "he's just fine."
Cruz says the public will decide if Trump is capable to serve, adding that any of the GOP candidates are better options than Democrat Hillary Clinton.
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7:54 p.m.
Donald Trump isn't able to list which aspects of the country's nuclear arsenal he'd put a priority on modernizing, only saying he'd employ someone "totally responsible who really knows what he or she is doing" to handle it.
Florida Sen. Marco Rubio is jumping in to help him, explaining that the country's nuclear triad, which includes silos, submarines and bombers, needs a "serious modernization" program.
Trump says the country must be "extremely vigilant and extremely careful" when it comes to nuclear power.
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7:53 p.m.
Chris Christie says in the Republican debate that he'd be much tougher on China than President Barack Obama.
Christie says Obama has done "nothing" in response to a massive data breach in which hackers infiltrated federal personnel records and information about millions who applied for U.S. security clearances. The Chinese government is widely believed to be responsible, though Beijing has denied it and the Obama administration has never publicly accused China as the culprit.
Christie says he would authorize hacks of Chinese computing systems and use the information to embarrass Beijing by showing the Chinese people how "corrupt" their government is.
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7:52 p.m.
Republican presidential candidate Carly Fiorina is saying some tough love with China could help the United States in further isolating North Korean dictator Kim Jung-un, since China is just as concerned about the young leader as the United States is.
The former Hewlett-Packard CEO says China recognizes strength. Fiorina suggests pushing back on China by retaliating against cyber-attacks on the United States, for one thing.
Retired neurosurgeon Ben Carson considers Kim Jong-un unstable and says the United States could use its economic power to "put him back in his little box where he belongs."
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7:50 p.m.
New Jersey Gov. Chris Christie says America's security should be the top priority in setting refugee policies, even if the Bible says to embrace those in need.
Christie is responding to a Texas Facebook user's question about how to reconcile the Bible with his position that America should not admit any Syrian refugees.
He says he's not backing away at all from that position, and says "the end of the conversation" for him was when the FBI director told Congress refugees can't be vetted effectively.
Christie also references the Bible's guidance on caring for widows and orphans, and says the San Bernardino attacks show "women can commit heinous, heinous acts against humanity, just the same as men."
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7:45 p.m.
Marco Rubio and Ted Cruz continue to clash over immigration during the Republican presidential debate.
In a heated exchange, the senators repeated attacks they have been making on the campaign trail. Texas Sen. Cruz criticized Florida Sen. Rubio for his work on a 2013 Senate bill that provided a path to citizenship to immigrants in the country illegally. Rubio argued that Cruz has also supported a legal status for some of those in the country illegally.
Pushed by Rubio on whether he would rule out ever legalizing people who are in the country illegally, Cruz said, "I have never supported legalization and I do not intend to support legalization."
Cruz and Rubio are both sons of Cuban immigrants.
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7:40 p.m.
Marco Rubio says he'd be open to allowing immigrants who entered the country illegally to obtain a green card after they have a work permit for at least 10 years, a position he says may not be in line with the majority of Republicans.
But Rubio says the process for giving people work permits can't even begin until the United States adequately secures the border and eases Americans' concerns about illegal immigration.
Immigration is a difficult issue for Rubio in the GOP primary. He co-sponsored a comprehensive immigration reform bill in 2013 that included a path to citizenship and has been widely panned by his Republican rivals.
He says securing the border requires 20,000 new border agents, 700 miles of additional fencing and a mandatory e-verify system for employers.
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7:35 p.m.
It's Jeb vs. Donald: Round 3.
At the Republican debate in Las Vegas, Jeb Bush again is slamming Donald Trump as unfit for the Oval Office. And this time Trump is blaming CNN for setting him up. The former reality show star says it's "sad that CNN leads Gov. Bush down a road by starting all of the questions, 'Mr. Trump this.'... I think it's very sad."
The two candidates ended up in a terse exchange far from the foreign policy questions at issue.
Bush retorted to Trump, "If you think this is tough and you're not being treated fairly, imagine dealing with (Russian President Vladimir) Putin."
Trump fired back, "Oh, you're a tough guy, Jeb."
Trump is reminding Bush of the wide gulf that separates them in presidential preference polls. He notes that at earlier debates, Bush stood near Trump at center stage because both were leading in the polls.
"You're started off here," Trump says, referring to the center. "You're moving further and further. Pretty soon you're going to be off the end."
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7:27 p.m.
Kentucky Sen. Rand Paul says, "if you're in favor of World War III, you have your candidate."
Paul directed the barb at New Jersey Gov. Chris Christie after he said he would shoot down Russian planes if they violated a no-fly zone over Syria.
Paul says that is a "recipe for disaster" and shows poor judgment. He also jabbed Christie over the 2013 George Washington Bridge lane-closing scandal, saying that also showed bad judgment. Christie hasn't been charged in the bridge scandal, but others close to him have.
Christie ignored the bridge reference. He says he would shoot down Russian planes if "they were stupid enough to think that this president was the same feckless weakling that the president we have in the Oval Office is right now."
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7:22 p.m.
Carly Fiorina says now is not the time to talk with Russian President Vladimir Putin.
The former Hewlett-Packard CEO says during the GOP debate that Putin respects strength, and she wouldn't engage him until she set up a no-fly zone in Syria, brokered a new deal with Iran and rebuilt the missile defense system in Poland "right under his nose," among other things.
New Jersey Gov. Chris Christie says he would be talking with Vladimir Putin plenty. Christie says he wouldn't hesitate to shoot down a Russian plane if one entered a Syria no-fly zone. Christie is also taking the opportunity to call President Barack Obama a "feckless weakling."
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7:20 p.m.
Donald Trump says the U.S. needs to focus on one thing at a time, and should take out Islamic State militants before fighting Syrian President Bashar al-Assad.
The business mogul is responding to a question at the GOP debate about how he could support leaving Assad in power and still say he likes winning. The debate moderator says leaving Assad in place means Iran and Hezbollah are winning.
Trump says Assad is a "very bad guy" but also says the U.S. has no idea about the identity of the anti-Assad rebels it's arming. He says the Islamic State must be dealt with first.
New Jersey Gov. Chris Christie counters that America should focus its attention on Iran, and says the Islamic State came about because of Assad and his Iranian sponsors.
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7:15 p.m.
Jeb Bush says he still believes getting rid of Saddam Hussein in Iraq was a good deal. Rand Paul's not so sure.
Bush says the lesson from the Iraq war is that the United States must have a "strategy to get in and get out." But Paul is questioning whether the United States should be toppling regimes in the first place.
Paul says, "out of regime change you get chaos," creating a place for radical Islam to thrive. Paul calls the discussion of whether the United States should pursue regime changes one of the "fundamental questions of our time."
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7:12 p.m.
Ben Carson is offering an air travel analogy to explain why he thinks the United States should focus on domestic needs.
Asked if the Middle East is better with dictators in charge, Carson says no one is better off with dictators, but the United States should "start thinking about the needs of the American people."
Carson likened the situation to putting on an oxygen mask on in a plane during an emergency, before helping a neighbor.
"The fact of the matter is the Middle East has been in turmoil for thousands of years," said the former pediatric neurosurgeon. "For us to think that we're going to go in there and fix that with a couple of little bombs and a few little decorations is relatively foolish."
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7:10 p.m.
Bashar al-Assad is a popular subject in the Republican presidential debate.
Ted Cruz repeated his position that he'd prefer Assad remain president of war-torn Syria. John Kasich is mocking that the answer, saying Assad "must go."
Donald Trump is jumping in in with his argument that the U.S. spends too much blood and treasure in the Middle East.
Trump also says the Syrian civil war is a complicated distraction from the effort to combat the Islamic State.
"I think Assad is a bad guy," Trump says. "I think we're backing guys who we have no idea who they are."
Trump says, "We have to get rid of ISIS first."
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7:05 p.m.
Ted Cruz is defending his position that the U.S. is more secure with Syrian President Bashar Assad in power.
The Texas senator says in Tuesday's Republican debate that President Barack Obama, former Secretary of State Hillary Clinton and "far too many Republicans want to topple Assad."
He says if Assad is removed, the Islamic State will "take over Syria."
Cruz says the U.S. should "hunt down our enemies and kill ISIS" rather than create opportunities for them to grow.
His position puts him at odds with other Republicans, including Florida Sen. Marco Rubio, who has clashed with Cruz on numerous issues raised in the debate.
Rubio says he "will not shed a tear" if Middle Eastern dictators are removed.
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7:00 p.m.
Carly Fiorina says the country needs "someone who's made tough calls in tough times" as a commander-in-chief instead of first-term senators "who never made executive decisions in their life."
The former CEO of Hewlett-Packard says talking tough is not the same as being strong.
She also says she wants to bring back a "warrior class" of generals, including David Petraeus and Stanley McChrystal, who she says retired early because they told President Barack Obama things he didn't want to hear.
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6:55 p.m.
Boos from the crowd inside the presidential debate hall are befuddling Donald Trump, who has said he wants to kill the families of terrorists and close parts of the Internet in places such as Iraq and Syria where the Islamic State exists. He say he doesn't understand why the crowd would object to infiltrating terrorists' conversations.
He tells the crowd "these are people that want to kill us folks."
Trump's reaction comes after Kentucky Sen. Rand Paul reminded debate watchers that closing the Internet would require getting rid of the First Amendment and killing the families of terrorists would defy the Geneva Conventions.
Trump replies with a rhetorical question: "So they can kill us, but we can't kill them?"
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6:50 p.m.
Ben Carson says his experience as a pediatric neurosurgeon prepared him to make tough choices as a leader.
Asked if he could be "ruthless" as a commander in chief and order airstrikes that could kill children, Carson says that when he told children he'd have to take out a brain tumor "they don't like me very much, at that point. But later on they love me."
Pressed on whether he could order airstrikes that would kill children and civilians, Carson said he was prepared to be "tough, resolute, understanding what the problems are and understanding that the job of the president of the United States is to protect the people of this country."
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6:44 p.m.
Jeb Bush and Donald Trump are at it again in the Republican debate.
With Trump defending his proposal to target the families of terrorists, Bush is dismissing him as not a "serious" candidate.
Trump retorts that "Jeb is a very nice person." He says, "We need toughness" or else the U.S. will get "weaker, weaker and just disintegrate."
Bush answers: "You're not going to be able to insult your way to the presidency. That's not going to happen."
Bush says: "Leadership is not about attacking people and disparaging people. Leadership is about creating a serious strategy to deal with the threat of our time."
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6:38 p.m.
Ted Cruz and Marco Rubio are clashing over how best to combat the Islamic State.
Rubio says in Tuesday's Republican presidential debate that Cruz's plan "is not to lead at all."
But Cruz says the Islamic State and radical Islamic terrorism "will face no more determined foe than I will be."
Cruz says he wants to use "overwhelming air power to utterly and completely destroy ISIS," but that would not involve leveling cities where innocent civilians could be killed. Cruz says the goal "isn't to level a city," it's to "kill the ISIS terorrists."
But Rubio says terrorists can't be defeated only through air strikes. He says a ground force against the Islamic State should be made up "primarily" of "Sunni Arabs that reject them ideologicaly and confront them militarily."
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6:35 p.m.
Donald Trump says he wants to keep members of the Islamic State from using the Internet to recruit American fighters.
He says the government must work with "brilliant people" in Silicon Valley to keep IS fighters offline, even if it means shutting down parts of the Internet.
Trump is also calling out members of the media to stop calling IS fighters "masterminds" because, in reality, they are thugs and terrible people.
He says, "we should be able to penetrate the Internet and find out exactly where ISIS is."
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6:29 p.m.
Ben Carson is ducking a question about whether Congress was right to end the National Security Agency's bulk phone-records collection program.
Carson declined to answer when asked Tuesday whether Sen. Ted Cruz was right to vote to end the program or whether Sen. Marco Rubio was correct in supporting its continuation.
Carson says: "I don't want to get in between them. Let them fight."
Carson says he is in favor of monitoring anyplace where people who may be engaging in radical activities are gathered, including mosques, schools, supermarkets and theaters.
Carson says we are at war and "We have to get rid of all this PC stuff." He says America's enemies will "take advantage of our PC attitude and get us."
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6:26 p.m.
Chris Christie is continuing to use the Republican debate to emphasize his experience as a governor and federal prosecutor, this time slamming several senators on the stage.
Marco Rubio and Rand Paul are jousting over Senate votes on the government's authority to gather intelligence from Americans' communication. Christie is mocking them, and the Senate in general, for "endless debate about how many angels can dance on the head of a pin."
He says he's had to make decisions about "whether to use actionable intelligence," and he says New Jersey was constantly under threat after the attacks Sept. 11, 2001. He doesn't detail just what kind of intelligence he is privy to as governor, but says it's way more important than what the senators argued about.
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6:24 p.m.
Rand Paul says Marco Rubio is opening the country to more terrorist attacks with attempts to allow more legal immigration.
The Kentucky senator says Rubio tries to portray himself as strong on national security, but is actually the weakest because he promoted a broad immigration reform bill in 2013 and has opposed border security.
Paul says more restrictions on legal immigration might have prevented attacks such as the one in San Bernardino and on Sept. 11, 2011, and says Rubio has more of an allegiance to Democrats on immigration than he does to conservative policies.
The exchange comes as Rubio advocated the collection of phone metadata, which Paul opposes.
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6:23 p.m.
Ted Cruz is defending his bill that eliminated the bulk collection of phone data, saying it allows law enforcement to do more to search cellphones and Internet-based calls versus simply landlines. He says the focus is now on targeting the "bad guys," not the general populace and covers all phones, versus 20 percent to 30 percent of phones before.
But Marco Rubio isn't buying the Texas senator's explanation, saying the situation demands more tools, not less, including the ability to collect metadata. The Florida senator also says a debate being broadcast nationwide in front of millions of people isn't the place to talk about classified information.
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6:22 p.m.
New Jersey Gov. Chris Christie says fear is the "new normal" in the United States.
During the Republican debate, Christie is stressing his background as a former federal prosecutor and criticizing President Barack Obama. Noting the mass shooting in San Bernardino, Christie says if a "center for the developmentally disabled in San Bernardino is now a target for terrorists, that means everywhere is a target for terrorists."
Christie says the country needs a president who will "understand what actionable intelligence is going to look like and act on it."
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6:20 p.m.
Ohio Gov. John Kasich says it would have been a better use of time for world leaders to discuss destroying the Islamic State rather than climate change at a recent gathering in Paris.
Kasich says it's imperative that the United States "get moving" in working with European and Arab allies to take on the Islamic State.
At home, he says the country must give law enforcement, including the FBI and local officials, the tools they need to stop attacks before happen. He says it's essential to encourage Americans to talk to law enforcement when they see "red flags."
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6:18 p.m.
Florida Sen. Marco Rubio says President Barack Obama made the fight against the Islamic State worse with his address from the Oval Office last week following the San Bernardino attacks.
Rubio says the president's approach to combating the Islamic State is continuing the current approach "and that's not working."
Rubio is focusing his criticism on Obama, not any of his Republican rivals sharing the stage with him in Las Vegas in Tuesday's presidential debate.
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6:17 p.m.
Texas Sen. Ted Cruz says, "everyone understands" Donald Trump's proposal to stop Muslims from entering the U.S., temporarily and with exceptions. But he says legislation he introduced suspending refugees from countries with large Islamic State footprints for three years "is more narrowly focused at the actual threat, which is radical Islamic terrorism."
He quoted Franklin D. Roosevelt's grandfather, saying, "All horse thieves are Democrats, but not all Democrats are horse thieves." He says there are millions of peaceful Muslims living across the world in peaceful countries like India. He says, "It's not a war on a faith, it's a war on a political and theocratic ideology that seeks to murder us."
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6:15 p.m.
Jeb Bush and Donald Trump are engaging in the first head-to-head battle of the night. Trump is defending his immigration policy " including his proposal to indefinitely ban all Muslims from entering the country. And he's repeating his plan for a wall at the Mexican border.
He suggests President Barack Obama has welcomed Islamic terrorists into the nation. "They're gone" under a Trump administration, he says.
Bush retorts that Trump's proposal is "not serious" and would make the U.S. less safe. "Donald is great at the one-liners, but he's a chaos candidate, and he'd be a chaos president," Bush says, noting that Kurds, potential allies in a battle against the Islamic State, "are Muslims."
Trump's response: Bush is coming after me only because I'm leading and his campaign has been a "total disaster" and "nobody cares."
Bush also calls Trump "unhinged." Trump responds that he's "the most solid person up here."
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6:12 p.m.
Republican presidential front runner Donald Trump says in his opening remarks at the GOP debate that he has sparked a "very big discussion that needed to be opened up" on "radical Islamic terrorism."
The former reality show star did not directly note his proposal to block Muslims from coming into the United States " temporarily, and with exceptions " that has taken a central role in the race. But he says: "People like what I say. People respect what I say."
Florida Sen. Marco Rubio says that if he's elected president, the country will have a commander in chief who believes the U.S. is the greatest country in the world.
Rubio says the current president wants the country to be "more like the rest of the world."
He says that, as a result, "you have millions of Americans that feel left out and out of place in their own country. "
Ben Carson is applying his experience as a neurosurgeon to foreign policy challenges. He compares his complex patient cases to the battle against Islamic State militants. He says he frequently faced life-and-death situations. Carson is also asking Congress to declare war on the Islamic State.
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6:02 p.m.
Former Florida Gov. Jeb Bush is pitching himself as a serious leader who has what it takes to keep the country safe and rebuild the economy. He says "serious times require strong leadership," including restoring funding cut from national defense and destroying the Islamic State.
New Jersey Gov. Chris Christie is pointing to the closure of public schools in Los Angeles Tuesday. He says that's evidence that President Barack Obama and former Secretary of State Hillary Clinton have not done enough to keep people safe. More than 1,500 school buildings in Los Angeles were shut for a day and searched after an emailed threat of violence. They will reopen Wednesday.
Texas Sen. Ted Cruz is using his opening statement in the Republican presidential debate not to attack his GOP opponents, but to say any of them would be better than Obama or Clinton, the Democratic front-runner. Cruz says America needs a president who understands the threat of the Islamic State. He promises to "utterly destroy" the militant group and stop terrorist attacks before they occur.
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5:55 p.m.
Kentucky Sen. Rand Paul is opening the Republican presidential debate by going after Donald Trump and Florida Sen. Marco Rubio. Paul says Trump is wrong in calling for censoring the Internet and Rubio should not advocate taking bulk phone data from Americans. Paul says the way to defeat terrorism is "by showing that we do not fear them."
John Kasich is playing the role of unifier-in-chief. Before the Ohio governor mentions anything about national security ?" which his rivals are giving top billing "? he says the nation's priorities are "creating jobs, making sure people can keep their jobs, the need for rising wages." And he says there's "too much yelling" in politics to solve those problems. "We'll never get there if we are divided" along party lines, he says. "Before all of that," he says, "we're Americans."
Carly Fiorina says all of the country's problems and wounds can be healed by a tested leader such as herself, citing her experiences beating breast cancer, burying a child and climbing the corporate ranks to eventually become CEO of Hewlett-Packard. Fiorina says she's been called "every B-word in the book" and has refused to take no for an answer.
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5:48 p.m.
The prime time Republican presidential debate is underway and the nine candidates are giving opening statements.
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5:39 p.m.
Some Republican Party leaders are increasingly nervous about the prospects of Donald Trump as the party's standard-bearer. But national GOP Chairman Reince Priebus is sticking with the role of party cheerleader tonight in Las Vegas.
"This is a unifying message," he tells the audience at The Venetian. He adds, "I think you can agree with me, that every single one of the candidates on this stage would be world better than Hillary Clinton."
The crowd applauded.