Building 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.
Trump weighed in on Twitter, insisting Mexico will pay for the wall "but at a later date so we can get started early."
"The Democrats don't want money from budget going to border wall despite the fact that it will stop drugs and very bad MS 13 gang members," he wrote.
Watch: White House Chief of Staff confident on wall negotiations
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 shutdown 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.
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Record low approval
The fight this time comes as the White House is eager to show off Trump's accomplishments at the 100-day mark.
The president is planning a speech to the nation and an "America First" rally on Saturday to highlight his successes, accompanied by an outpouring of digital content.
Trump surprised his own aides this week by promising a big announcement on tax reform on Wednesday even though lawmakers have yet to conclude negotiations on health reform, a major variable in government spending.
Mulvaney said it would be a statement of principles rather than legislation, "with some indication what the rates are going to be."
"I don't think anybody expects us to roll bill language on Wednesday," he added.
Although he has slashed government regulations and used his executive powers more frequently than any of his recent predecessors, Trump has had no major legislative achievements to speak of so far.
His attempt to repeal and replace his predecessor health care reforms was rejected in the Republican-controlled Congress, and his executive order imposing a travel ban targeting citizens of several mainly Muslim countries as well as refugees has been blocked by the courts.
A new Washington Post/ABC News poll showed his approval ratings to be at a record low for a modern US president at a point in office when most have still enjoyed a honeymoon.
It found that 42 percent of Americans approved of his performance and 53 percent disapproved.
Spending compromise?
Democrats have shown little interest in compromise, particularly on the border wall project.
"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.
However, Mulvaney insisted that "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," Kelly said on CBS's "Face the Nation."
"We have tremendous threats, whether it's drugs, people, potential terrorists, coming up from the south."
Sessions said Trump would decide whether the wall money was worth the risk of a government shutdown.
"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."
