WASHINGTON — The Republican health-care overhaul spearheaded by House Speaker Paul Ryan of Wisconsin and backed by President Trump hung in the balance Wednesday, as the White House signaled at the eleventh hour a willingness to rework the measure to mollify conservatives.

After insisting for weeks that the changes sought by hard-right members would render the bill unable to pass the Senate, White House officials and Republican House leaders appeared to shift their thinking – and opponents agreed to keep working on a deal with the goal of holding a floor vote in the House by Thursday night.

Rep. Mark Meadows, R-N.C., chairman of the conservative House Freedom Caucus, said he had taken personal calls Wednesday from Trump seeking a resolution, though he said no formal offer had been extended by the White House.

“We are working very diligently tonight to try and get there,” Meadows said Wednesday.

“The president has been profoundly engaged,” said Rep. Trent Franks, R-Ariz. “I think things are going in a very good direction right now.”

More than two dozen House conservatives remained opposed or leaning against the effort to revise the Affordable Care Act, even as a handful of moderates decried the current proposal as harming the elderly and poor. Both the president and vice president made personal appeals throughout the day to secure the votes needed to pass the House.

Pence huddled with members of the Freedom Caucus in his Eisenhower Executive Office Building office early in the day, while Trump met with 18 House Republicans at the White House, but these efforts appeared to produce just one definitive aye vote from the conservative camp: Rep. Steve King, R-Iowa.

Republican leaders can afford only 22 defections, given that one Democrat is expected to be absent Thursday. A Freedom Caucus spokeswoman said that “more than 25” members of the group oppose the bill.

The day’s events laid bare party leaders’ struggle to muster enough votes for one of their defining goals: to roll back the 2010 health-care law that helped galvanize conservatives in the years since to wrest control of both the legislative and executive branches from Democrats.

If Republicans fail this initial test of their ability to govern, Trump and Capitol Hill Republicans may face a harder time advancing high-priority initiatives on infrastructure, tax reform and immigration. They might also find themselves navigating strained relationships among themselves.

For much of Wednesday, the Freedom Caucus’s message, spokeswoman Alyssa Farah tweeted, was: “start over.”

At the same time, three more Republican moderates – Reps. Frank LoBiondo of New Jersey, Daniel Donovan of New York and David Young of Iowa – announced their opposition Wednesday, increasing pressure on leaders to win over the conservatives.

Ryan summoned more than a dozen members of the moderate Tuesday Group to his office late Wednesday evening in an apparent bid to curb further defections.

“There’s not enough votes to pass this,” Meadows said. “Nothing’s changed.”

Conservatives are seeking to eliminate more of the ACA’s insurance mandates, known as “essential benefits,” which require plans to cover specific medical benefits, such as mental health care, prescription drugs and preventive care. That, conservatives argue, is the only reliable way to force down premiums.

Ryan warned in an interview Wednesday with conservative radio host Hugh Hewitt that fulfilling those Republican demands would violate Senate budget rules and leave the bill vulnerable to a blockade by Democrats.

“Our whole thing is we don’t want to load up our bill in such a way that it doesn’t even get considered in the Senate,” the speaker said. “Then we’ve lost our one chance with this one tool we have.”

That stance appeared to soften later Wednesday, as White House officials and House leaders tried to negotiate changes to the bill that would get closer to conservatives’ goal of eliminating more of the Affordable Care Act’s insurance mandates.

“We’re not there yet,” Meadows said Wednesday, “but we’re very optimistic that if we work around the clock between now and noon tomorrow that we’re going to be able to find some common ground. Tonight is an encouraging night, and yet I don’t want to be so optimistic to say that the deal is done, but I do think that there is a framework to work with our leadership and the leadership in the Senate and certainly the administration to find some common ground.”

He continued: “The overall impression of the Freedom Caucus is we’re willing to jump through unbelievable hurdles to hopefully get to a point where this bill is better for the American people.”

Even if the House approves the package, the legislation faces an uphill battle in the Senate – and the new negotiations late Wednesday raised the possibility that the challenge would only grow at the other end of the Capitol. There are at least a dozen skeptics of the bill among Senate Republicans, who maintain a slim 52-to-48 advantage in the Senate, and many of them want to maintain some of the Affordable Care Act’s more generous spending components. Republicans can afford to lose the votes of only two senators, assuming Pence would step in to cast a vote for the health-care rewrite in the case of a tie.

In addition to conservatives, who do not think the proposal does nearly enough to undo the ACA, some moderates fear it will harm their constituents as well as their party’s prospects at the ballot box.

Earlier in the day, even as opposition appeared to persist, White House press secretary Sean Spicer told reporters that the measure would pass the House, adding there is no Plan B if the proposal goes down.

“There is Plan A and Plan A,” said Spicer, who described Trump as “the closer” for the deal. “We’re going to get this done.”

Complications stemming from the bill’s last-minute tweaks appeared to add yet another political headache Wednesday, as veterans’ groups discovered that the latest draft might make them ineligible for a tax credit. A change made to ensure the measure would comply with Senate rules created a separate consequence – that individuals would qualify for the bill’s tax credits only if they “are not eligible” for other types of coverage, including those provided by Veterans Health Administration.

In an email, House Ways and Means Committee spokeswoman Lauren Aronson said the issue would be fixed in subsequent legislation. “This amendment makes no change to veterans’ health care. In working with the administration and the Veteran Affairs Committee, we will continue to ensure that America’s veterans have access to the best care available.”

Carlos Fuentes, legislative director for Veterans for Foreign Wars, said veterans want the issue resolved before any bill becomes law. “It would be a huge impact on veterans if this were not corrected,” he said.

Elsewhere in the Capitol Wednesday, Republican leaders were working to clear the bill’s final procedural hurdle. House Rules Committee Chairman Pete Sessions, R-Texas, said the measure would allow Americans “to make their own health-care decisions” and create the kind of competitive insurance market that will expand health-care coverage without excessive government mandates.

But Rep. Jim McGovern, D-Mass., questioned why lawmakers would move it to the floor when the Congressional Budget Office had not yet issued a new analysis of the bill in light of tweaks the majority made to it on Monday. Also unknown were the additional impacts on coverage and federal spending of the provisions still being negotiated on Wednesday.

“I don’t think we should be meeting on a bill when we don’t even know how many people it will hurt,” said McGovern, whose motion to adjourn was defeated by a vote of 7 to 2.

Sessions predicted that the congressional scorekeeping would come out sometime Wednesday night: “We will not go to the floor without that CBO score.”

Trump made a public pitch for the measure Wednesday during a panel in the Roosevelt Room with the newly confirmed Centers for Medicare and Medicaid Services director, Seema Verma, and female medical professionals.

When a reporter asked whether he would keep trying to overhaul the ACA if the House bill failed, the president replied, “We’ll see what happens.”

During the Rules Committee session Wednesday, Republicans acknowledged the legislation would undergo even more changes before it reaches Trump’s desk.

“This isn’t a once and forever bill, or vote, or anything of the kind,” said Rep. Tom Cole, R-Okla. “What we do today isn’t going to be the final word.”