But some other conservatives are undecided and have met with Mr. Johnson in his Capitol office. They have vented their frustration over the spending drama that unfolded late last month and urged the speaker to commit to institutional changes that would prevent GOP leaders from forcing another huge spending bill on lawmakers.

Those undecided conservatives include Rep. Andy Harris of Maryland, chairman of the far-right Freedom Caucus; Chip Roy of Texas; Victoria Spartz of Indiana; Andy Biggs of Arizona; and Ralph Norman of South Carolina.

Adding to Mr. Johnson’s problems is that many of these lawmakers are considered wildcards within the House Republican Conference. Both Mr. Massie and Mr. Roy campaigned for Florida Gov. Ron DeSantis in the 2024 Republican primary and have previously fended off primary threats from President-elect Donald J. Trump, who has endorsed Mr. Johnson for speaker.

“Too many of my Republican colleagues operate out of fear,” Mr. Roy said on the campaign trail in Iowa. “I fear the Lord. I’m not afraid of politics. I am not afraid of political retaliation. Worst case scenario, I end up back in Texas? My life is pretty good.”

Mr. Biggs, the former Freedom Caucus chairman, has long angered Republican leaders. He opposed Kevin McCarthy’s ascension to speaker and voted to oust him ten months later.

Ms. Spartz is perhaps the most unpredictable. She frequently protests what she sees as Republican leaders in the House’s permissive approach to government spending. She announced late last year that she “will not sit on committees or participate in the caucus until I see Republican leadership in Congress.” She had previously announced that she would not run for re-election, only to have the decision reversed. And in Mr. McCarthy’s election, she initially voted for him, but later voted “present” on several ballots.