WASHINGTON — House Speaker Paul D. Ryan, facing a formidable new impediment thrown in his path by the Congressional Budget Office, worked Tuesday to line up support for his bill to repeal the Affordable Care Act.

The CBO on Monday predicted an increase of 24 million people without health insurance by 2026 under the Republican plan, but also forecast $337 billion in deficit reduction over the same period, a better-than-anticipated assessment that House Republican leaders hoped would help quell a revolt from their most conservative members. A vote could come next week.

Ryan, a Wisconsin Republican, was counting on that deficit reduction — as well as tax cuts for high earners and insurance and medical device companies — to entice members whose Republican constituents have been itching to see the current law crumble.

“I think what we unite upon is much greater than what divides us in this,’’ Representative Kevin Brady, Republican of Texas and the chairman of the Ways and Means Committee, which is responsible for part of the repeal measure, said Tuesday on Fox News. “We have some ideas that have been brought to us, and I certainly have worked with our House conservatives to make major changes already in this.’’

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. If he can do that, the Senate would almost certainly alter the bill significantly, a fight likely to take weeks.

He is facing critics from different factions in his party, including conservatives who say the bill does not represent the wholesale replacement of the law that was pledged, and more moderate members concerned about thousands of constituents losing coverage.

But Ryan is also counting on President Donald Trump, who he talks to almost daily, to woo conservatives to win passage of the bill in the House, and then ostensibly leave it to Senate Republicans to decide if they want to be the ones to refuse to honor a longstanding Republican promise to repeal the law.

Tom Price, the secretary of Health and Human Services, and House committee leaders attended a Senate Republicans’ lunch Tuesday to drum up support for the new health care bill.

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

Whether presidential intercession would succeed in aiding passage remains an open question, but Tuesday, several of the most conservative members of the House continued to voice their opposition. “I’m a no,’’ Representative Dave Brat, a Virginia Republican, said in an interview Tuesday. “The CBO report doesn’t really affect my calculation too much.’’

The budget office’s judgment on rising ranks of the uninsured and a short-term spike in insurance premiums did seem to rattle the calculations of some Senate Republicans, especially those from states that expanded their Medicaid program under President Barack Obama’s signature health law, who are increasingly worried about the loss in benefits for their constituents.

Despite the welcomed surprise on the size of deficit reduction, a central goal of the Tea Party movement that helped propel many of those members into Congress, conservatives in the House continued to oppose the bill. The budget office’s report said the bill would contribute to higher premiums in 2018 and 2019, but reduce premiums after that, so that in 2026 average premiums would be about 10 percent lower than under current law.

“Politically, that’s pretty hard to stomach,’’ Brat said, noting that the House bill would take several years to slow the growth of premiums that were rising rapidly under the Affordable Care Act. The bill, he said, does not take steps that could really save money: eliminating requirements for certain “essential health benefits’’ and making it easier for consumers to buy insurance from other states.

Representative Mo Brooks, Republican from Alabama, said on CNN that the GOP health bill was “still the largest welfare program ever proposed by the Republican Party,’’ adding, “Let’s be clear about something. The fact that the Republican welfare plan is not as bad as Obamacare does not mean that it’s good. It is not good.’’

But the very elements of the bill that conservatives, whose votes will be needed for final House passage, find so disturbing are the very things worrying Republican Senators, who have a far broader base of constituents, many in red states who have benefited from the health care law.

“The CBO estimate that millions of Americans could lose their health insurance coverage if the House bill were to become law is cause for alarm,’’ said Senator Susan Collins, Republican of Maine. “It should prompt the House to slow down and reconsider certain provisions of the bill.’’

In an interview with the conservative radio host Hugh Hewitt, Senator Tom Cotton, Republican of Arkansas, who is one of the Senate’s most conservative members, said he did not think the bill would reduce premiums for working people, calling the measure a “flawed bill’’ with little chance of passage in the House.

“I suspect they don’t have anything close to a majority of their members who are willing to vote for this bill now,’’ Cotton said. “I know many of them, and they come from all stripes. They’re not just hard-line conservatives. Many of them are centrists, or many of them are just being practical-minded about this bill the way I am.’’

He also panned the plan by Ryan to follow a three-step strategy to repeal and replace the Affordable Care Act, which assumes that Democrats will provide votes to pass additional bills at a later date that would help complete the replacement of the law. Cotton firmly rejected the idea that Democrats would agree to pass “some mythical legislation in the future.’’