"If the President can't defend this country, then he cannot fulfill his constitutional oath of office," Miller said.
Miller said that by September 2020, "hundreds of miles" of new barriers will have been built along the border. And he suggested that if Congress passes a resolution disapproving of the emergency, Trump would probably veto it.
"He's going to protect his national emergency declaration, guaranteed," Miller said.
Still, Democrats have vowed to fight Trump on what they say is executive overreach, echoing a joint statement issued by House Speaker Nancy Pelosi and Senate Minority Leader Charles Schumer.
"Frankly, the president is trying to take the power of the purse away from the legislative branch," Senator Tammy Duckworth said on ABC News' This Week. "We are coequal branches of government, and he is trying to do a type of executive overreach, and it's just really uncalled for."
Duckworth said that even if one agreed with Trump that there is an emergency at the southern border, a wall would not be the most effective way to address it.
"If he wants to appropriate more money to put folks - more agents at the border to put more people at the ports of entry ... we can have those conversations," Duckworth told host Martha Raddatz. "But to take money away from (the Department of Defence) in order to build this wall that is essentially a campaign promise, I think, is really wrong priorities and I think it's very harmful to the country."
As examples, Duckworth listed several projects that could be jeopardised by the diversion of funds to construct a border wall - a list that Pelosi's office is in the process of amassing, the Hill reported.
Congressman Adam Schiff pointed to Trump's own comments that he didn't need to do declare a national emergency.
"He's pretty much daring the court to strike this down," Schiff said. "It is going to be a real test for my GOP colleagues in Congress and their devotion to the institution. If we surrender the power of the purse, there will be little check and no balance left. It will not be a separation of power anymore - it will be a separation of parties."
Republicans have been split on the issue, with some fully backing Trump and others cautioning that allowing an emergency declaration now would set a precedent for future Democratic presidents to do the same for myriad other issues.
"This is an emergency. I mean, what are we on now? The fifth caravan?" Congressman Jim Jordan said on This Week, referring to groups of migrants from Central American countries who have marched toward the United States' southern border, mostly to seek asylum. "So, I would just ask those senators: How many caravans do we need? Six or seven or ... the one that never stops?"
Senator Lindsey Graham said on CBS News' Face the Nation that he supported Trump's decision to "go that route" and declare a national emergency, even if the diversion of military construction funds to build a border wall meant jeopardising projects such as the construction of a middle school in Kentucky and housing for military families.
"I would say it's better for the middle school kids in Kentucky to have a secure border," Graham said. "We'll get them the school they need. But right now we've got a national emergency on our hands."
Representative Will Hurd, whose district includes more than 1285km of the US-Mexico border, said on Face the Nation that he opposes Trump's declaration of an emergency, warning that it "sets a dangerous precedent."
"I don't think we needed a national emergency declaration. That is not a tool that the president needs in order to solve this problem," Hurd said.
Hurd noted that Congress has already made decisions about how to appropriate funds to the military. He voiced concern about diverting that money to build the wall.
"Our government wasn't designed to operate by national emergency," he said. "We're almost in uncharted territory."
The national emergency declaration also has divided Americans, triggering at least one protest in New York, with various groups promising to hold more across the country on Presidents' Day.
Acting defence secretary Patrick Shanahan said he would soon start to examine projects that could be delayed or cancelled to free up funds for border activities.
California Attorney-General Xavier Becerra, a Democrat, said that he was working with several other states to take legal action against the White House and that a filing was "definitely and imminently" coming.
"We are prepared. We knew something like this might happen," Becerra said. "And with our sister state partners, we are ready to go."
When asked whether California would have standing to challenge the declaration, because Trump appears to be focused on building a wall in Texas, Becerra said, "We're confident there are at least 8 billion ways that we can prove harm," referring to the number of taxpayer dollars that Trump is looking to divert.
"It's become clear that this is not an emergency, not only because no one believes it is, but because Donald Trump himself has said it's not," Becerra said.
"But there is enough evidence to show that this is not the 9/11 crisis that we faced back in 2001; it's not the Iran hostage crisis we faced in 1979. It's not even the type of national emergency where we are trying to take action against a foreign enemy or to avoid some type of harm befalling Americans abroad."
THE LAWSUITS
The advocacy group Public Citizen filed a lawsuit in US District Court in Washington, seeking to block Trump's declaration on behalf of three Texas landowners and an environmental group.
"We just sued Trump over his fake national emergency," the group stated. "If Trump gets away with this, there's no telling what the next concocted 'emergency' will be, who will be targeted and what emergency powers will be claimed."
Another advocacy group, Citizens for Responsibility and Ethics in Washington, sued the Justice Department for allegedly failing to provide documents - including legal opinions and communications - related to the President's decision to declare a national emergency.
"Americans deserve to know the true basis for President Trump's unprecedented decision to enact emergency powers to pay for a border wall," the group's executive director, Noah Bookbinder, said. "The Justice Department's inadequate response raises major questions about whether even the president's own administration believes there is a legal basis for him to bypass the constitutional authority granted to Congress to appropriate funds."
The Centre for Biological Diversity, an environmental group, filed another lawsuit in federal court, saying the President has failed to identify a legal authority to take such an action, "and Congress has not enacted any emergency legislation even remotely related to border wall construction, and thus the President's reallocation of funds is unlawful."
The group's complaint also warned that a border barrier would prevent wildlife from being able to freely pass in their natural habitat "and could result in the extirpation of jaguars, ocelots, and other endangered species within the United States."
The American Civil Liberties Union said it was preparing a lawsuit for early this week, arguing that Trump cannot legally redirect taxpayer money during an "emergency" unless it's for military construction projects that support the armed forces.