During the tenures of both George W. Bush and Barack Obama, some of the most influential dealmakers in the Senate — Edward M. Kennedy, Democrat of Massachusetts, and John McCain, Republican of Arizona, among them — tried repeatedly to forge a compromise that would increase border security and provide a path to legalization for millions of undocumented immigrants.
But public sentiment had shifted among Republicans and their constituents despite the support for an immigration overhaul from the top of the party. The deals either collapsed in the Senate or were never even brought up in the House, where sentiment against anything that could be branded as “amnesty” runs deep.
“It just all blew up and fell apart,” said Senator Johnny Isakson, Republican of Georgia and a participant in bipartisan immigration talks in 2005 who remembered getting bricks for a border wall sent to his office in protest of his effort to forge a deal.
Stymied legislatively, Mr. Obama in 2012 instituted DACA via executive order. Mr. Trump promised to reverse it if elected and he did so, providing a window until March 5 to find a permanent solution. That is what led to the shutdown crisis, with Democrats trying to use their leverage over spending to get an acceptable resolution.
Democrats say that twice in recent weeks and another time last year, Mr. Trump appeared to consent to at least the outlines of an agreement that would provide permanent protection for those immigrants. But then he quickly reversed course upon consultation with the hard-line advisers on immigration who have the president’s ear once Democrats depart.
Mr. Schumer said that in a White House luncheon meeting Friday, he offered significant concessions for the DACA legislation, including a large increase in Pentagon spending as well as an agreement to meet the president’s demand for money for the border wall with Mexico that Democrats had previously refused. Democrats say the White House rejected the proposal hours later, asserting that it did not go far enough to limit the ability of new immigrants to bring in more relatives to live in the United States.
The president’s shifting positions have left Democrats exasperated.
“I essentially agreed to give the president something he has said he wants in exchange for something we both want,” Mr. Schumer said on Sunday.
Republicans say that this situation is different from ones that led to previous immigration failures, and that they are fully committed to negotiating in good faith when the shutdown is ended.
“Now we have a deadline and we have bipartisan willingness to deal with the issue,” said Senator John Cornyn of Texas, the No. 2 Republican. “I think it’s different.”
Both Republicans and Democrats say Mr. Trump’s endorsement of any immigration deal is essential, since it is the only way a sufficient number of House Republicans could be enticed to vote for it under cover of Mr. Trump’s backing.
“That makes it easier for House action,” said Senator Jeff Flake, an Arizona Republican who has been part of the latest round of bipartisan immigration talks. “I think if he finds a way to like it, they can pass it in the House.”
But Mr. Trump’s backing is no guarantee of Republican votes. And even if he does endorse a plan, Republicans worry that he could change his mind at any time.
Senator Tom Cotton, an Arkansas Republican who has been a major impediment to an immigration compromise with Democrats, said Sunday on NBC’s “Meet the Press” that he could not commit to back a proposal simply because the president endorsed it. And some on Capitol Hill believe that Speaker Paul D. Ryan’s leadership post would be in jeopardy if he pushed through an immigration bill that most House Republicans opposed.
In recent months, Republicans suggested that they would hold a strong hand in any funding showdown because Democrats would be reluctant to force a government shutdown over undocumented immigrants. If Democrats did, Republicans figured they would have a strong message to counter with by attacking Democrats as willing to shortchange Americans to help those who entered the country illegally.
They are now aggressively pressing that line of assault. But the message is also provoking new doubts about the sincerity of Republican determination to help Dreamers, muddying an immigration debate that is at the center of the conflict and has confounded Washington for almost 20 years.