Funding for the wall was Trump's signature campaign promise, and the White House appeared determined to get Congress to approve a down payment as part of a bigger bill to keep the US government funded.
White House budget chief Mick Mulvaney said the administration is prepared to make concessions to Democrats on health care reform in order to get the wall money.
But if the wall isn't funded, will the president veto the larger spending bill, risking a government shut down on Saturday -- coincidentally Trump's 100th day in office?
"Don't know yet," Mulvaney said on Fox News Sunday. "We are asking for our priorities and importantly we are offering to give Democrats some of their priorities as well."
The specter of a government shutdown has often loomed over US budget negotiations. The threat has most often been averted -- but has come to pass several times, most recently for 16 days in 2013 amid a dispute over funding for Barack Obama's signature health care reforms.
Democrats showed little interest in a compromise this time around.
"I hope the president will back off," said Senator Dick Durbin, the number two Democrat in the Senate, on CNN's "State of the Union."
"To think that he would consider shutting down the government of the United States of America over this outlandish proposal of a border wall, which we can't even pay for at this point, and is opposed by Democrats and Republicans all along the border, that would be the height of irresponsibility," he said.
Mulvaney insisted, however: "Shutdown is not desired and it's not a tool, it's not something we want to have.
"We want our priorities funded and one of the biggest priorities during the campaign was border security, keeping Americans safe and part of that was a border wall."
US Attorney General Jeff Sessions and Homeland Security Secretary John Kelly made similar pitches on other television talk shows.
"I think it's certainly worth hard negotiation over," said Kelly on CBS's "Face the Nation."
"We have tremendous threats, whether it's drugs, people, potential terrorists, coming up from the south. And some type of a barrier, an effective barrier backed up by the brave and very effective men and women of DHS, I believe is essential."
Sessions said Trump would decide whether the wall money was worth risking a government shutdown for.
"But I know one thing, we need that wall," he said on ABC's "This Week." "It will help us complete the promise that the president has made to the American people. That's what they want."