With the deal, Republicans concerned about the nation’s debt and deficits were essentially left empty-handed, even with a Republican in the White House and Republicans controlling both houses of Congress.

On Capitol Hill, conservatives vented on Friday morning at a closed-door meeting in which the Treasury secretary, Steven Mnuchin, and the president’s budget director, Mick Mulvaney, sought to drum up more Republican support for the legislation.

“There were probably a lot of members in there sort of in disbelief” watching the pitch from Mr. Mnuchin and Mr. Mulvaney, said Representative Ryan A. Costello, Republican of Pennsylvania. “It’s kind of, ‘Where am I right now?’”

Mr. Mulvaney was an outspoken fiscal conservative while in the House. Mr. Costello described Mr. Mnuchin, a former hedge fund manager and Goldman Sachs executive who has given money to Democrats, as a “longtime Democratic donor Treasury secretary.”

“If it wasn’t so serious,” Mr. Costello added, “it kind of would have been funny.”

The House vote passed 316-90, with all of the no votes cast by Republicans. It came a day after the Senate passed the measure and about 48 hours after Mr. Trump blindsided the Republican leaders — Senator Mitch McConnell of Kentucky, the majority leader, and Speaker Paul D. Ryan — abruptly siding with Democratic leaders to support a short-term debt limit extension.

Conservatives in the House had already been fuming over the idea of raising the debt ceiling without spending cuts or other conservative policy changes.

“What you have is two competing things,” said Representative Mark Meadows, Republican of North Carolina and the chairman of the hard-line House Freedom Caucus. “You’ve got a compassionate heart that wants to deal with hurricane relief, and you’ve got a number of very principled people who realize we’re bankrupting our country by continuing to raise a debt ceiling and not doing anything about spending.”