As 2023 opened with Republicans newly in control of the House, the far-right members of the party considered themselves empowered when it came to federal spending, with increased muscle to achieve the budget cuts of their dreams.

But it turned out that many of their Republican colleagues did not share their vision of stark fiscal restraint. Or at least not fervently enough to go up against a Democratic Senate and White House to try to bring it into fruition.

Instead, Speaker Mike Johnson on Friday pushed through a $1.2 trillion bipartisan package to fund the government for the rest of the year, with none of the deep cuts or policy changes that ultraconservatives had demanded. Those on the right fringe have been left boiling mad and threatening to make him the second Republican speaker to be deposed this term.

“The speaker failed us today,” declared Representative Thomas Massie, Republican of Kentucky, after one of his ultraright colleagues, Representative Marjorie Taylor Greene, Republican of Georgia, filed a measure to potentially force a vote to remove Mr. Johnson, over a spending plan she called “atrocious” and “a betrayal.”

The vote and its bitter aftermath brought to a head the simmering tensions among congressional Republicans about difficult spending issues, including whether to force a government shutdown to try to achieve their budget aims — a divide that once again has sent House Republicans spiraling into chaos.

The looming challenge to Mr. Johnson from within sparked quick recriminations from other Republicans, who accused their colleagues of sowing discord that harms their own party and its chances of success in a pivotal election for control of Congress in November.