“We don’t have a deal yet, and so until we have a deal, I don’t think we’ll know exactly what the coalition will look like to get it passed,” said Representative Dusty Johnson of South Dakota, a top McCarthy ally. “But listen, Kevin McCarthy understands how conservative his conference is. He is going to deliver a deal that is going to be embraced by the vast majority of his conference.”

As negotiators inched closer to a deal, hard-right Republicans were openly expressing concern that Mr. McCarthy would sign off on a compromise they would view as insufficiently conservative. Several right-wing Republicans have already vowed to oppose any compromise that retreats from cuts that were part of their debt limit bill, which would slash domestic spending by an average of 18 percent over a decade.

“Republicans should not cut a bad deal,” Representative Chip Roy of Texas, an influential conservative, wrote on Twitter, shortly after telling a local radio station that he was “going to have to go have some blunt conversations with my colleagues and the leadership team” because he did not like “the direction they are headed.”

Representative Ralph Norman of South Carolina said he was reserving judgment on how he would vote on a compromise until he saw the bill, but added, “What I’ve seen now is not good.”

Former President Donald J. Trump, who has said that Republicans should force a default if they do not get what they want in the negotiations, also was weighing in. Mr. McCarthy told reporters he had spoken briefly with Mr. Trump about the negotiations — “it came up just for a second,” the speaker said. “He was talking about, ‘Make sure you get a good agreement.’”