Many Republicans on Capitol Hill are not so sure.
In interviews with CNN, a number of Republicans suggested that Trump's claim amounted to wishful thinking, saying they believed the billionaire businessman would ultimately backtrack on one of his central campaign promises.
"I doubt that they're going to pay for it," said Utah Sen. Orrin Hatch, the longest-serving Senate Republican, referring to Mexico. "There's a lot he could do if he wanted to (force Mexico's hand). In all honesty, I don't think that's going to happen."
Rep. Mike Coffman, a Colorado Republican, added: "I never thought that would happen. I thought it was a gimmick."
And some conservatives warned Trump would face a backlash if he failed to follow through.
"I'm for building a wall," said Rep. Mo Brooks of Alabama. "And I'm for Donald Trump keeping his promise to the American people that Mexico pay for it." He added that he would be "disappointed" if Trump failed to deliver.
House GOP sources tell CNN that Trump's transition team has urged Republican leaders to include funding for the wall in a spending package
that must pass by April 28 in order to keep the government open. The price tag is uncertain, but some similar proposals have been projected to cost upwards of $10 billion.
Trump insists his rhetoric is no gimmick, telling The New York Times Friday that Mexico will reimburse the United States, using negotiations over revamping the North American Free Trade Agreement as leverage against the country. He has also previously warned of imposing punitive measures on Mexico if the country does not comply.
"We're going to get reimbursed," Trump said. "But I don't want to wait that long. But you start, and then you get reimbursed."
Top Republican leaders were cautious in their assessment, including Texas Sen. John Cornyn, the No. 2 Senate Republican.
"Well right now, they're pretty uncertain as to what all of this means," Cornyn said of his constituents in his border state. He said he urged Trump's nominee for secretary of the treasury, Steve Mnuchin, to "make sure there aren't any unintended consequences of this."
"About 6 million American jobs depend on cross-border trade with Mexico," Cornyn told CNN.
Some House conservatives also were skeptical.
Asked if he believed that Trump would succeed in persuading Mexico to pay for the wall, Rep. Dave Brat of Virginia said: "Not in some big, they're going to hand us a big check kind-of-way." But he added: "There'll be a policy in place where we can compensate the cost they're imposing."
Even getting the funding bill through Congress could be difficult. House Minority Leader Nancy Pelosi said Friday the plan would be a "tough sell" to Democrats. And Senate Minority Leader Chuck Schumer is waiting to discuss the matter more fully with his caucus, but he'd have the power to block the measure in the Senate if he kept Senate Democrats largely in line against it.
But if Congress ends up stuck with the tab, it's clear some conservatives may not be happy.
"I'm for securing the border for the American people, and we're going to be sure we get that done," said Rep. Jim Jordan, R-Ohio, a member of the conservative House Freedom Caucus.
Asked if that meant he'd support Trump's plan to have Congress pay for it first, Jordan deadpanned: "I didn't say that." And he walked into an elevator.