WASHINGTON - The Republican health-care overhaul spearheaded by House Speaker Paul Ryan (Wis.) and backed by President Donald Trump hung in the balance Wednesday, as the White House signaled at the 11th 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 GOP 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.

GOP 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, four more Republican moderates - Reps. Charlie Dent (Pa.), Frank LoBiondo (N.J.), Daniel Donovan (N.Y.) and David Young (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 in an apparent bid to curb further defections. One participant, who spoke on the condition of anonymity to describe the private meeting, said Ryan and other House leaders described the potential deal with the Freedom Caucus, which would strip essential health benefits but leave other ACA mandates, such as those dealing with preexisting conditions and coverage of adult dependents, in place.

"People got to say their piece and react to the proposal. It's safe to say people had concerns about stripping out essential health benefits, especially at this late hour," the Tuesday Group member said. "I think they're short [of votes], and I think they're considerably short. . . . I'm not sure where all this goes tomorrow."

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 GOP 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 shift late Wednesday, when separate aides in the White House and the House GOP leadership said a new interpretation of Senate rules had raised the possibility that acceding to the Freedom Caucus's request might not threaten Senate consideration of the whole bill. But both aides said the provision could still be stripped out once the bill reaches the Senate.

Democratic Senate aides insisted that would be the case. "What the proponents aren't telling conservative House Republicans is that the plan to repeal essential health benefits will almost certainly not be permissible under Senate reconciliation rules," said Matt House, a spokesman for Senate Minority Leader Charles Schumer, D-N.Y.

In fact, 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.

"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."

An additional potential hurdle facing the bill is the updated analysis still to come from the Congressional Budget Office, which will reflect changes to the measure that were issued on Monday. That analysis could be rendered inaccurate if further changes are made before the vote.

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 that 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.

In another example of last-minute changes, Illinois' GOP delegation announced late Wednesday night that Centers for Medicare and Medicaid Services director Seema Verma had assured them that "Illinois will have the opportunity to accurately report its 2016 Medicaid payment information to CMS." The state "has long been disadvantaged by below average Medicaid reimbursements," the lawmakers said, and this adjustment will ensure that the state would receive more federal funds when the government shifts to allocating Medicaid dollars on a per-capita basis under the bill.

Elsewhere in the Capitol Wednesday, GOP 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 CBO had not yet issued a new analysis of the bill. 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.

Trump made a public pitch for the measure Wednesday during a panel in the Roosevelt Room with 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."

Many of the changes made to the bill so far were aimed at placating conservatives, including giving states the option to take a fixed Medicaid block grant and to impose work requirements on childless, able-bodied adults covered under the program. Others responded to broader concerns about the sufficiency of the tax credits offered to help Americans purchase insurance.

One revision was more narrowly targeted - added at the behest of Republicans from Upstate New York who wanted to end their state's practice of commandeering local tax revenue to fund state Medicaid benefits.

That concerned Donovan, who said a day after meeting with Trump in the Oval Office that he would oppose the bill.

In an op-ed for the Staten Island Advance, he said the change "gives our district short shrift" and also said the GOP bill would disproportionately harm older Americans.

"Seniors on fixed incomes would likely see a big jump in their healthcare expenses without a near-term reduction in premiums," he wrote. "We can't burden seniors who deserve better from us!"

The Washington Post's Abby Phillip and Lisa Rein contributed to this report.

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