WASHINGTON — Republican leaders scrambled for support on Tuesday ahead of a vote to take up legislation repealing the Affordable Care Act, negotiating, pressuring and cajoling Republican senators but preparing for another embarrassing setback for President Trump.

Republican leaders seemed to be taking a page from the playbook used to get a bill over the line in the House, trying to find ways to appease the most conservative members of their conference while pressuring moderates to fall in line with fewer concessions. Senator Mitch McConnell of Kentucky, the majority leader, cast his lot early on by allowing the bill to be more conservative than his moderate members wanted, setting the tone for the debate.

Conservatives now want to allow states to waive the Affordable Care Act’s prohibition on insurance companies charging sick people more for coverage and are asking for a more expansive waiver system for state regulators. They are also demanding more money for tax-free health savings accounts to help people pay for private insurance.

Senators from states that expanded the Medicaid program — and Senator Susan Collins, Republican of Maine — would most likely not brook many of those changes, especially the measure to severely undermine protections for people with pre-existing medical conditions. They want more money for mental health benefits for people addicted to opioids and money for states to cover people left behind by the rollback of the Medicaid program in both the House and Senate versions.

On Monday, three Republican senators — Ms. Collins, Rand Paul of Kentucky and Ron Johnson of Wisconsin — said they would vote against the motion to begin debate scheduled to hit the Senate floor on Wednesday, joining Senator Dean Heller of Nevada, who made the same pledge on Friday.

A bevy of other senators from both flanks of the party seemed headed in the same direction if they did not see changes made to the Senate health care bill, leaving the measure in deep peril, since Republicans can only lose two votes from their own party.

But House Speaker Paul D. Ryan, who won House approval for a repeal bill after a few false starts, expressed confidence in Mr. McConnell on Tuesday.

“I would not bet against Mitch McConnell,” Mr. Ryan said. “He is very, very good at getting things done through the Senate, even with this razor-thin majority. I have every expectation that the Senate — I don’t know what day — but I have every expectation the Senate will move this bill.”

The release of a Congressional Budget Office evaluation on Monday did little to help leaders roll up votes from either side of the fence. The budget office said the Senate bill would leave 22 million more uninsured after 10 years, while sending out-of-pocket medical expenses skyrocketing for the working poor and those nearing retirement.

The budget office did not provide conservatives with support for their demands either. The state waivers already in the Senate bill “would probably cause market instability in some areas” and “would have little effect on the number of people insured” by 2026, the analysis concluded. Adding still more waivers, including one that could allow insurers to price the sick out of the health care market, could deprive even more people of health care.

White House officials were bracing for the increasing likelihood that the procedural vote would fail and they would have to take the measure back up after the Fourth of July recess — when they hoped to be able to woo Mr. Johnson, who has been a surprisingly fierce critic of the bill from the right. The senator has repeatedly warned that this week is too soon to vote on the health care measure, as Republican senate leaders have insisted they need to do.

Just as he did with the House when the far right and a small group of moderates both prevented initial passage of a bill, Vice President Mike Pence, who has attended most of the Senate Republican Tuesday lunches — and quietly hosted senators and House members for a…