WASHINGTON — President Trump insisted on Tuesday that he remained committed to his hotly disputed plan to build a wall along the Mexican border, despite backing off a demand that the project be funded in a short-term spending measure that must be passed by Friday to avoid a government shutdown.
By easing off the proposal for a down payment on wall construction, Mr. Trump may have cleared one of the biggest obstacles to passage of the spending bill before financing for most government operations expires at the end of the week.
Still, the president did not want his acquiescence to be seen as a sign that he was any less committed to the project. “Don’t let the fake media tell you that I have changed my position on the WALL,” he wrote on Twitter Tuesday morning. “It will get built and help stop drugs, human trafficking etc.”
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Mr. Trump told a group of conservative journalists at the White House on Monday evening that he might accept a spending bill that included money for border security without setting aside as much as he had sought for the wall.
The current spending legislation would keep the government operating through the end of the fiscal year on Sept. 30. But the president could refocus his battle for wall construction in spending bills for the next fiscal year.
“Building that wall and having it funded remains an important priority to him,” Kellyanne Conway, the president’s counselor, said on “Fox & Friends” on Tuesday morning. “But we also know that that can happen later this year and into next year. And in the interim, you see other smart technology and other resources and tools being used toward border security.”
Democrats welcomed Mr. Trump’s decision not to hold out for the money this week. “It would remove the prospect of a needless fight over a poison-pill proposal that members of both parties don’t support,” Senator Chuck Schumer of New York, the minority leader, said on the Senate floor.
The promise to build a wall — or actually to extend a series of barriers that already exist on part of the border — was a central theme of Mr. Trump’s campaign last year. Not only would he protect the United States from a tide of immigrants coming across the border illegally, he said, Mexico itself would pay for it.
But the cost estimates for the wall have gone up, and Mexico has made clear it has no intention of spending money on it.
Sean Spicer, the White House press secretary, said on Monday that Mr. Trump was still determined to make Mexico pay, but that he would proceed first with American tax dollars.
“The president has been very clear” that “in order to get the ball rolling on border security and the wall, that he was going to have to use the current appropriations process,” Mr. Spicer said. “But he would make sure that that promise would be kept as far as the payment of it.”
So, he was asked, Mexico will eventually pay? “That’s right,” Mr. Spicer said.
Mr. Trump initially estimated during the campaign that the wall would cost $12 billion, but the figure has soared since then. A Department of Homeland Security internal report in February estimated that the wall could cost about $21.6 billion. A new report issued by Senate Democrats last week put the cost far higher, at nearly $70 billion.
Even without the wall, illegal crossings of the Southwest border have been falling drastically.
The number of people apprehended fell 40 percent from January to February and again 30 percent from February to March, according to the Customs and Border Protection agency. The White House has attributed that to Mr. Trump’s tough talk and bolstered enforcement. Since November, when Mr. Trump was elected, illegal crossings have fallen by nearly 75 percent.
As lawmakers on Capitol Hill continued feverish negotiations on Tuesday, White House and Senate staff members seemed to agree that the wall had been reduced to something like a metaphor for broad-based border security funding, which is all but certain to end up in a final spending package.
Senator Mitch McConnell of Kentucky, the Republican leader, suggested that Congress could well meet its Friday night deadline to get a funding package completed. “These talks have been part of a bipartisan bicameral process from the start,” he said. “I look forward to more productive conversations with senators, our House colleagues and the White House so that we can get this important work done soon.”
But other issues remain.
Most notable is the fate of payments to health insurers to lower deductibles and other costs for low-income consumers who buy plans through the marketplaces created under the Affordable Care Act. Mr. Trump has threatened to withhold the subsidy payments, which are the subject of a lawsuit, as leverage in negotiations with Democrats whose votes will be needed to pass any spending bill in the Senate.
Democrats have now turned that threat on its head, insisting that the payments — which the administration has quietly continued to make — be guaranteed as part of any deal. “Six million people could lose their health care, which could become unaffordable,” Mr. Schumer said.
There also is a dispute over health benefits for retired miners who face the loss of their coverage, an issue that led to a near-shutdown last year. Senator Joe Manchin III of West Virginia and other Democrats want those benefits extended, and miners have been a big constituency for Mr. Trump.
Democrats would also like to see Congress bail out Puerto Rico’s ailing Medicaid program as part of the deal.
But lawmakers on both sides of the aisle have strikingly avoided the sort of inflamed talk that is often a part of fights over budgets, suggesting that Republicans and Democrats alike have gotten much of what they wanted in the spending bill.