WASHINGTON – House Republican leaders said Wednesday that they plan to bring their controversial plan to revise key parts of the Affordable Care Act to a vote on Thursday, capping weeks of fits and starts in their attempt to fulfill a signature campaign promise.

The flagging Republican effort to reshape the nation’s health care system picked up steam Wednesday, as GOP leaders tried to address concerns about people with preexisting medical conditions. But independent analysts remained skeptical that the new proposal would fully address the needs of at-risk patients who receive coverage guarantees under the Affordable Care Act, underscoring the controversial nature of the Republican effort.

Republican leaders huddled in the office of House Speaker Paul Ryan, R-Wis., Wednesday evening to figure out the next steps after a whirlwind day at both ends of Pennsylvania Avenue. Several said they would hold a vote this week only if they felt certain it could pass – meaning they now believe they have the votes.

Exiting the relatively brief leadership meeting House Majority Leader Kevin McCarthy, R-Calif., guaranteed victory.

“Do we have the votes? Yes. Will we pass it? Yes,” he told reporters.

Rep. Fred Upton, R-Mich., an influential Republican, was putting the finishing touches on his proposal to provide more financial assistance – $8 billion over five years – to people with preexisting medical conditions. Those people are at risk of losing protections under the GOP plan, which seeks to repeal and replace major parts of the ACA.

Just a day earlier, Upton said he could not support the Republican plan because of preexisting conditions. But he sounded an optimistic note after sketching out his fix Wednesday and meeting with President Donald Trump at the White House.

Long said Trump called him Tuesday afternoon. The two had a “good give and take,” he said and Trump grew “a little angry” when he said he could not support the bill. But eventually, he said, they came to an agreement on his amendment.

Rep. Billy Long, R-Mo., who like Upton was against the bill earlier this week because of preexisting conditions, was also in the White House meeting. Now supportive of the bill, he cautioned: “There’s still work to be done on the votes, I believe.”

A Washington Post analysis showed 20 House Republicans either opposed to or leaning against the bill late Wednesday, and 36 more either undecided or unclear in their positions. If no Democrats support the bill, House Republicans can lose no more than 22 GOP votes to pass their bill.

Upton’s amendment was not met with resistance by the House Freedom Caucus, a key bloc of conservatives whose opposition to an earlier version of the health care bill led GOP leaders to yank the measure.

“I don’t see any defections because of this particular amendment from our previous whip count,” said Rep. Mark Meadows, R-N.C., the chairman of the group. Meadows and Upton both said they had been in touch.

Under the GOP plan, states could opt out of the parts of the ACA, meaning that people with preexisting conditions could be denied coverage or charged more. Such states would have to set up high-risk pools to absorb some of the costs.

Upton’s amendment would help some patients with expensive conditions such as cancer or diabetes pay premiums and out-of-pocket costs.

But some experts doubted that $8 billion was enough to aggressively address those costs. According to an analysis from the Kaiser Family Foundation, the temporary high-risk pool created by the ACA covered just 100,000 people; the government paid out $2 billion in subsidies to that pool in one year.

Far more people with preexisting conditions are likely to lose health coverage under the GOP health care plan — some estimate around 5 million — and depending on how many states apply for the funds, $1.6 billion a year could be spread thin.

“For subsidies to cover 68 percent of enrollees’ premium costs, as ACA tax credits do now in the individual market exchanges, the government would have to put up $32.7 billion annually,” wrote Emily Gee, a health economist at the progressive Center for American Progress, in an analysis of the Republican plan. “Even after applying that subsidy, high-cost consumers would still owe $10,000 annually toward premiums.”

After meeting with Trump, Upton said his amendment would “more than cover those who might be impacted.”

There was also uncertainty about how the bill would be scored by the nonpartisan Congressional Budget Office – which measures how much the legislation will cost and how many people stand to lose coverage.

Republican leaders appeared willing to move ahead with a vote even before obtaining an updated score. Speaking on the House floor Wednesday afternoon, Majority Leader Kevin McCarthy, R-Calif., brushed off a Democrat’s concerns about a new score, noting that a previous version of the bill had already been reviewed by the CBO.

The House is slated to go on recess Thursday until May 16, forcing GOP leaders to quickly make a decision about whether to try to hold a vote before leaving town or put it off until lawmakers return.

The White House has been putting heavy pressure on Ryan to swiftly pass a health care bill, amid fears that Republicans will lose their window of opportunity if the effort continues to drag out.

Trump dispatched top administration officials to the Capitol on Wednesday, including Vice President Mike Pence; White House budget director Mick Mulvaney; Administrator of the Centers for Medicare and Medicaid Services Seema Verma; and Health and Human Services Secretary Tom Price.

Democrats, who have held firm against the GOP’s repeal and replace push, said they were not impressed by the newly proposed changes.

“Trumpcare means heart-stopping premium increases for people with pre-existing conditions and no band-aid amendment will fix it,” said House Minority Leader Nancy Pelosi, D-Calif., who like many in her party have sought to associate the bill closely with Trump.

The Upton change is the latest fix Republicans have added to their measure as they’ve tried to keep it viable. Last month, they added $15 billion for a program to reimburse insurers who cover patients with preexisting conditions – an effort to appease conservatives worried about lowering premiums.

It remained unclear whether all states would be able to apply for the newly proposed funding, or just states where patients with preexisting conditions could be charged higher premiums. Under a separate proposed amendment to the bill from Rep. Tom MacArthur, R-N.J., which convinced many conservatives to sign onto the bill, states could apply for a federal waiver from a ban on insurers charging those patients more.

Even if the bill clears the House, it will face a steep climb in the Senate, where there is widespread disagreement among Republicans about how to proceed on health care.

Rep. Carlos Curbelo, R-Fla., a moderate seen as a top Democratic target in 2018, was jawboned several times by party whips and told reporters that he could be convinced to move from no to yes.

“The easiest thing to do in this town is to say no,” he said. “That’s usually the politically expedient thing to do. If I believe this legislation can be improved by the time it comes back to the House, I will be supporting it.”

Rep. Mike Coffman, R-Colo., who represents a swing district in suburban Denver that voted for Hillary Clinton, offered mixed reviews in a written statement.

“If House Leadership will work to tighten protections for those with preexisting conditions, I’m a yes on sending this bill to the Senate for further consideration,” he said in a statement Wednesday. “If not, I’m a no, and we’ll go back to the drawing board.”

The Washington Post’s John Wagner, Kelsey Snell, Paul Kane, Ed O’Keefe and Amber Phillips contributed to this report.