Inside the White House, this person said, there are fairly regular conversations about who will replace Tillerson even as he remains in the job. CIA Director Mike Pompeo, for example, may no longer be the leading choice because it means he would not brief Trump every day, and the president likes him in that role, the official said.
"I think our allies know at this point he's not really speaking for the administration," this Trump official said - a particularly sharp slap given that Tillerson has sought to be a buffer and interpreter for allies angry or bewildered by some of Trump's actions.
West Wing officials spoke about Tillerson on the condition of anonymity to describe internal personnel dynamics.
Raj Shah, a White House spokesman, said Trump "is very pleased with his entire national security team, which includes Secretary Tillerson."
State Department spokeswoman Heather Nauert said Tillerson "enjoys a strong relationship with the president. Most importantly, they share a commitment to the denuclearization of the Korean peninsula, the security of our homeland and the protection of our allies."
Nauert noted that Tillerson had lunch with Trump on Thursday. The discussion included North Korea, she said.
The latest dust-up began Tuesday when Tillerson caught the White House by surprise with remarks at the Atlantic Council that appeared to mark a shift away from the Trump administration's demand that North Korea commit to disarmament upfront. Tillerson's comments also stood in sharp contrast to Trump's past pronouncements that talking to North Korea is a trap or waste of time.
"We're ready to talk anytime North Korea would like to talk," Tillerson said. "We're ready to have the first meeting without preconditions."
"Let's just meet and let's - we can talk about the weather if you want," Tillerson said to laughter.
The comments upset Trump and several senior aides, and set off a cascade of emails and phone calls that ended with a terse statement from press secretary Sarah Huckabee Sanders. National Security Council aides were particularly frustrated with the remarks and complained loudly, administration officials say.
"The President's views on North Korea have not changed. North Korea is acting in an unsafe way not only toward Japan, China, and South Korea, but the entire world," Sanders said in the statement. "North Korea's actions are not good for anyone and certainly not good for North Korea."
Senior Trump aides say that Tillerson knew he was contradicting Trump, according to White House advisers. The State Department said Tillerson's invitation was not a break with the administration's official position.
Tillerson's State Department continues to clash with the White House over personnel - picks are often scuttled or delayed, officials say - and Trump will sometimes react with exasperation when the secretary's name is brought up, other officials said. One senior official said Trump will sometimes commend senior policy aide Stephen Miller for the time he clashed with Tillerson, or will mention disagreements Tillerson has had with other aides - and not take Tillerson's side.
Inside the West Wing, several aides said people close to Trump essentially were counting down the days until Tillerson leaves, which they guess will be in February.
Trump has told advisers he is amazed at the negative news attention Tillerson receives and has said to at least one adviser that Tillerson probably gripes about him behind his back. But Trump does not believe Tillerson called him a "moron" as NBC News first reported, a White House official said.
Tillerson has sought out Sen. Bob Corker, R-Tenn., as an ally, frequently meeting with him for breakfast. And Corker has tried to solidify Tillerson's standing by vouching for him to Trump and senior aides. But after Corker went on television and praised Tillerson, Trump complained to aides that Corker was defending the secretary of state.
For now, Trump has told advisers that he is not firing Tillerson.
"Where's our Rex?" he told supporters at a recent holiday party, according to audio obtained by The Washington Post. "Rex is doing a great job!"
Tillerson received applause at the event.
During an October visit to China, Tillerson had described US willingness to talk with North Korea as a linchpin in any nonmilitary resolution to the nuclear crisis. Within hours, Trump had hung his top diplomat to dry with a tweet.
"I told Rex Tillerson, our wonderful secretary of state, that he is wasting his time trying to negotiate with Little Rocket Man," Trump wrote, using a favorite insult for North Korean leader Kim Jong Un. "Save your energy, Rex, we'll do what has to be done!"
Sanders later underscored to reporters that the White House sees no opening for talks except to try to free Americans detained in North Korea.
West Wing aides have cited that example as well as policy clashes behind closed doors to criticize Tillerson for overstepping his role or freelancing on policy issues.
Rumors have swirled since this summer that Tillerson is on thin ice and would soon leave the administration. He has dismissed them as Washington backstabbing and rumor-mongering, saying this month that news reports about an impending ouster were "laughable."
"People need to get better sources," Tillerson said in a Dec. 2 interview with the Reuters news agency.
At the State Department on Wednesday, Nauert said Tillerson was "on the same page" with the White House.
"Diplomacy is our top priority," Nauert said. "We remain open to dialogue, and we've long said this. We remain open to dialogue when North Korea is willing to conduct a credible dialogue on the peaceful denuclearization of the Korean Peninsula."
Nauert added that "we are not seeing any evidence that they are ready to sit down and have those kinds of conversations right now."
An open-door policy is just what many US allies and partners want, and what outside policy experts have frequently recommended as the best way to draw Kim to talks that could avert war.
They argue that Kim is likely never to agree at the outset that eliminating his nuclear arsenal is the goal of talks. Kim has used his rapidly advancing nuclear weapons capability to threaten the United States and Asian allies, and has vowed never to give them up.
Speaking to State Department employees Tuesday, Tillerson did not sound like a man with one foot out the door. He said he plans to travel to Canada next week and to Africa and Latin America early next year.
"This is all about modernizing the department and making it easier to complete your mission," Tillerson told employees.
He will attend a United Nations Security Council session on North Korea in New York on Friday.
One adviser who knows Tillerson and Trump well said the president had treated the secretary of state "horribly" and had humiliated him unnecessarily. But this person said Tillerson also had made "enough mistakes of his own."
"It makes me angry," this person said of the president's behavior toward Tillerson, describing Trump as "impulsive" and Tillerson as "a patrician Boy Scout," two who are never going to get along - but that it doesn't need to be so public.
