After a fractious period in the Capitol — cresting this month with Democrats’ filibuster of Mr. Trump’s Supreme Court nominee, Justice Neil M. Gorsuch, and Republicans’ deployment of the so-called nuclear option to confirm him — members seemed modestly hopeful for a reset of sorts.

“This is a good time to stabilize the government,” said Senator Roy Blunt, Republican of Missouri and a member of the Appropriations Committee. “And then whatever debates we didn’t have in the next three days, we could have in the next three months or three years.”

As lawmakers on Capitol Hill continued 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 Lindsey Graham, Republican of South Carolina, praised Mr. Trump for relenting.

“He’s not going to overplay his hand,” Mr. Graham said. “Here’s the challenge to the Democrats: Are you going to overplay your hand?”

At the very least, Democrats seemed inclined to declare victory on the wall for now.

Mr. Schumer — whose caucus is delighting this week in pointing out areas in which Mr. Trump has fallen short of campaign promises as he approaches his 100th day in office — exulted on Tuesday in the wall’s near-term fate. “For weeks, we have been making good progress in negotiating with our Republican colleagues,” Mr. Schumer said. “The president’s 11th-hour demand threatened to upend the progress. We’re pleased he’s backing off.”

At the same time, Mr. Trump took care to avoid the appearance of acquiescence on the wall, eager to reinforce his long-term commitment. “Don’t let the fake media tell you that I have changed my position on the WALL,” he wrote on Twitter on Tuesday morning. “It will get built and help stop drugs, human trafficking, etc.”