The House voted Tuesday to pass a resolution to terminate President Donald Trump's national emergency proclamation to build the border wall, presenting their opening salvo in a battle that's expected to drag into the next presidential campaign, both in the courts and on Capitol Hill.

The bill passed 245-182, with just 13 Republicans joining 232 Democrats to approve the measure.

The measure now heads to the Senate, where its prospects are less certain. Even if it does pass the upper chamber, Trump has vowed to veto the measure.

Given Tuesday's tally in the House, it's unlikely Congress would have the two-thirds majorities needed to override a veto.

House Speaker Nancy Pelosi told reporters that Trump's "power grab usurps" the legislative branch's constitutional responsibilities and "fundamentally violates the balance of power envisioned by our founders."

"We would be delinquent in our duties if we did not resist, if we did not fight back to overturn the president's declaration. To not do that would be to abandon our own responsibilities. We do not intend to do that," Pelosi, D-Calif., said Monday. "What the president is saying about the border is mythology. It's not reality, but this is not about the wall. Whatever you think about the wall, think about the Constitution of the United States."

Even Senate Republicans have been questioning the president's authority in declaring a national emergency.

Senate Majority Leader Mitch McConnell described what he called a "robust and vigorous" discussion during a private lunch on Tuesday with Vice President Mike Pence and a Department of Justice lawyer who briefed Senate Republicans on the president's emergency declaration.

"I haven't reached a total conclusion," McConnell said when he was asked if he considered the president's move to be a legal one. "What is not in doubt is we have a serious crisis at the border, and our colleagues across the aisle are in denial.”

At least three Republican senators -- Susan Collins of Maine, Thom Tillis of North Carolina and Lisa Murkowski of Alaska -- have said they will vote in favor of the resolution.

Many Republicans have expressed their concerns about the president’s ability, under the declaration, to move funds that have already been appropriated by Congress. They've also said they are concerned about the precedent it could send should a Democrat become president.

In a Washington Post op-ed, Tillis announced he would vote in support of the joint resolution.

"As a U.S. senator, I cannot justify providing the executive with more ways to bypass Congress. As a conservative, I cannot endorse a precedent that I know future left-wing presidents will exploit to advance radical policies that will erode economic and individual freedoms," Tillis wrote. "These are the reasons I would vote in favor of the resolution disapproving of the president's national-emergency declaration, if and when it comes before the Senate."

Murkowski said Trump is "overstepping into the legislative prerogative."

"We as legislators need to be concerned about that separation," she said. "We need to be concerned about preserving those clear lanes that are outlined within the Constitution. This is not about whether or not I support President Trump."

Trump declared a national emergency at the southern border on Feb. 15, taking executive action to obtain billions of dollars for his border wall on top of $1.4 billion Congress sent him earlier this month for border fencing.

"We do have an emergency," Trump told a gathering of governors at the White House on Monday. "We have an emergency of people pouring into our country that we don't want -- criminals, smugglers. We have drugs pouring into our country. We can't have it."

Democrats still aren't buying it.

"There is no crisis at the border," House Majority Leader Steny Hoyer, D-Md., insisted. "The issue [Tuesday] will be whether there is a crisis of our constitutional adherence, whether there is a crisis because there is a lack of conscience and courage among the members of the House of Representatives and subsequently the United States Senate to stand up for what the Founding Fathers wanted. They did not want King George."

The Senate is expected the considered the measure in the coming weeks, setting up another showdown with Trump.

Rep. Justin Amash, one of the few Republicans supporting the resolution in the House, told ABC News Live many of his peers agree with the substance of the measure but worry about a political cost in breaking with the president.

"Behind the scenes, privately, many of them are very concerned about what the president is doing. And they understand our constitutional system and they would, I think, love the opportunity to oppose him," Amash, R-Mich., said on ABC News' "The Briefing Room" on Tuesday. "They have that opportunity here, and I think they’re not going to take it for political purposes. They're worried about what might happen back home with Republican voters."

Amash, who considers himself a constitutional conservative, says there are "fair arguments" for tighter border security but that only Congress has the power to appropriate taxpayer funds.

"The president doesn’t get to just declare an emergency for something congress has deliberated many times over the past several years. The president signed legislation that Congress passed that did not have the funding he wanted. He didn’t veto the legislation. You can’t not veto the legislation and then say there’s an emergency," Amash said. "You should have vetoed it in the first place. You have to make sure each branch stays in its own lane."

Rep. Raul Ruiz, D-Calif., told ABC News Live that Democrats are pushing the measure to terminate the emergency declaration in order to prevent Trump from setting a precedent.

"What we’re doing here is going towards using the Constitution and the checks and balances to protect Article 1 [of the Constitution] and Congress’ role of determining what gets spent and to prevent the overreach and a power grab by the president who is trying to bypass the Constitution," Ruiz said.