The changes sought by Senate Republicans could upend White House efforts to shore up support from Mr. Ryan’s conservative flank. On Tuesday, several of the most conservative members of the House continued to voice their opposition.

“Leadership’s public positions have pretty much been ‘this is the bill, take it or leave it’ kind of approach,” said Representative Mark Meadows, Republican of North Carolina and chairman of the House Freedom Caucus, adding, “I have no indication that it has changed.”

And if changes are not made, conservatives are balking.

“I’m a no,” Representative Dave Brat, Republican of Virginia, said in an interview on Tuesday. “The C.B.O. report doesn’t really affect my calculation too much.”

Mr. Ryan’s calculus at this point is less strategic (how to actually get a bill that would replace the health care law to final passage) than tactical (how to muster enough votes to get the measure through the chamber he leads).

House Republicans portrayed the intraparty divisions as minor.

“I think what we unite upon is much greater than what divides us in this,” Representative Kevin Brady of Texas, chairman of the Ways and Means Committee, which is responsible for part of the repeal measure, said on Fox News Tuesday.

Mr. Ryan is counting on Mr. Trump, whom he talks to almost daily, to help win passage of the bill in the House. The speaker would then leave it to Senate Republicans to decide if they want to be the ones to refuse to honor the longstanding Republican promise to repeal the law.

Mr. Trump, though, has remained leery of Mr. Ryan since the campaign, when the speaker publicly voiced skepticism about Mr. Trump. That point was reinforced this week when Breitbart News, a right-wing website and frequent Ryan critic, released comments by Mr. Ryan from October that were critical of Mr. Trump.

And House conservatives continued to oppose the bill, which Representative Mo Brooks, Republican of Alabama, described in an interview with CNN as “still the largest welfare program ever proposed by the Republican Party.”