A short-term measure, approved by the Senate and awaiting action this week in the House, is attached to a larger, yearlong spending bill that increases the Pentagon’s budget by nearly $20 billion and provides funding to the Departments of Labor, Education and Health and Human Services. By allowing Mr. Trump to claim a win on military spending, legislators hope to avert a veto.

“I think he’ll sign it,” Senator Richard C. Shelby, Republican of Alabama and the chairman of the Senate Appropriations Committee, said Tuesday.

Mr. Trump has publicly flirted with the idea of shutting the government down for months. At a rally this month in Montana, he said he would “most likely” not force a shutdown. Then he told reporters he would have “no problem” shutting the government down and noted that a number of conservative pundits believe it would be a “great political issue.”

Congressional Republicans, acutely aware that they could be in for bruising midterms, are convinced that a shutdown before the November elections would be politically calamitous and have sought to persuade the president to push that battle to December. Even some of the president’s hard-line immigration allies, including the Freedom Caucus chairman, Representative Mark Meadows, Republican of North Carolina, agreed. Mr. Meadows said this month it would be “more prudent” to debate border security after the midterms.

A shutdown is “not in anyone’s interest, and he knows that,” Speaker Paul D. Ryan of Wisconsin said of Mr. Trump.