House Speaker Paul D. Ryan said Wednesday that his health-care proposal must change to pass the House, marking a significant retreat from his earlier position that the carefully crafted legislation would fail if substantially altered.

Ryan acknowledged that changes would be made two days after an analysis issued by the Congressional Budget Office prompted a fresh round of criticism of his proposal. Among the report's projections was that 14 million fewer Americans would be insured after one year under the Republican plan.

Speaking after a private meeting of GOP lawmakers, Ryan said that leaders would "incorporate feedback" from the rank-and-file in response to the CBO findings. He did not repeat his previous comments calling support for the bill a "binary choice" for Republican lawmakers.

"Now that we have our score we can make some necessary improvements and refinements to the bill," he said, referring to the CBO's estimate of the effect on the number of those covered by health insurance and what the GOP proposal would cost.

Ryan did not detail what changes are under consideration to his plan.

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What's next for the Obamacare replacement bill

Vice President Pence also spoke to House Republicans in the meeting, acknowledging that the White House was open to changes in the legislation, which heads to the House Budget Committee for approval Thursday. President Trump has offered his support for Ryan's measure, while still meeting with conservative lawmakers who have expressed serious doubts about the plan.

"This president is ready to put the full weight of his bully pulpit and all of his tools" behind the bill, Pence told Republicans, according to Rep. Kevin Cramer (R-N.D.). "It was very important for us to hear that, because there are a lot of people who need that shoring up."

Earlier in the day, Pence told conservatives at a private lunch meeting of the Republican Study Committee, a large caucus of conservative House Republicans, that the plan was still under negotiation, according to several ­attendees.

"As he said, it's not often that we get an opportunity to undo such a big piece of legislation that had negative consequences on the American people," said Rep. Markwayne Mullin (R-Okla.), paraphrasing Pence's message. "He's open to make improvements. . . . Anything that can get 218 votes and make the bill better, we're all about it."

Pence's visit to Capitol Hill — which included meetings with influential blocs of Republicans as well as individual members — came as part of a White House effort to salvage support for the embattled American Health Care Act, even as Trump's conservative allies told him the bill could be a political trap.

Ryan aides played down his remarks, saying that the speaker had long acknowledged further changes were possible as the bill moved through a multistep legislative process.

"As the speaker has repeatedly said, this bill will work its way through regular order and while the structure will remain intact, modifications will happen during the legislating process," spokeswoman AshLee Strong said. "But the reality remains: Members will face a binary choice to either vote for a bill that can pass or vote for Obamacare status quo."

The legislation will face an important test Thursday, when the Budget Committee will decide whether to advance it to the House floor. The committee may not directly amend the bill but may make nonbinding recommendations. Any substantive changes would be made by the House Rules Committee, which controls how the bill is presented and debated on the floor.

House Budget Committee Chairman Diane Black (R-Tenn.) insisted that GOP leaders are not "dug in" when it comes to concerns about the measure.

"We're listening; we're definitely listening," she said Wednesday to the conservative radio host Hugh Hewitt. "And I will tell you: Tune in to our Budget Committee tomorrow, and you will hear these conversations."

The blitz came two days after the CBO estimated that 24 million fewer Americans would be insured over the next 10 years under the GOP plan. The falling coverage numbers and estimates of higher premiums for older and low-income Americans raised concerns among many lawmakers, particularly those representing states that expanded eligibility for Medicaid under the Affordable Care Act.

Ryan plans to hold a House floor vote next week, and Trump administration officials have spent the past two days in near-constant discussions with Republican lawmakers as they scramble to find enough votes to pass the measure. Leaders were set to take a preliminary count of members supporting the bill Wednesday night.

Critics of the legislation warned Wednesday that the measure remains far short of the 216 votes needed for passage. Typically, 218 votes are needed to pass a bill in the 435-member House, but five pending vacancies have reduced that threshold. No Democrats are expected to support the bill, and with 237 Republicans, party leaders can afford no more than 21 ­defections.

"They will whip it, and they will find 40 nos and another 30 or 40 undecideds," said Rep. Mark Meadows (R-N.C.), chairman of the hard-right House Freedom Caucus, who has called for ­changes to mollify conservatives.

One member of the Budget Committee who belongs to the Freedom Caucus, Rep. Dave Brat (R-Va.), said he will vote against the bill in committee. Two other Freedom Caucus members, as well as three others on the panel, have not said how they will vote.

One conservative Budget Committee member who has voiced concerns about the bill said Wednesday that he had been persuaded to advance it.

Rep. Glenn Grothman (R-Wis.) said he would support the legislation in the panel based on an "implied promise that things are going to be different on the floor, and therefore we can keep the process moving."

He declined to say exactly who had made that promise: "People higher up on the food chain than me."

"I'll say this, if the bill that comes to the floor is the exact same one in Budget, I'll feel a little bit that I'd been had," he said.

House Majority Whip Steve ­Scalise (R-La.) acknowledged in an interview with MSNBC on Wednesday that the bill remains under ­negotiation.

"Watching sausage being made is not the prettiest thing," he said. "What can we do on those final pieces that are being negotiated with President Trump and a number of our members in our conference that ultimately want to get to a yes vote and send this bill over to the Senate?"

Ryan spent much of Tuesday and Wednesday giving interviews in an attempt to drum up support for the plan. On the Fox Business Network, he defended the plan as a collaboration with Trump and the Senate and said that "the major components are staying intact" while opening the door to "refinements and ­improvements."

Later, in an interview with the conservative radio host Laura ­Ingraham, he countered reports that the White House's support for the bill might be slipping. Ryan said he had spoken to White House Chief of Staff Reince ­Priebus and Trump's chief strategist, Stephen K. Bannon, "a number of times" about the bill, and he noted that Trump had brought lawmakers to the White House multiple times to make the case for the legislation.

"We are on the same page as the White House," Ryan said. "I think there are those who would love to wedge us for one reason or another, but that's just not the case."

Hours later, at a rally for Affordable Care Act opponents outside the Capitol, Sen. Ted Cruz (R-Tex.) told activists that the House plan "has a lot of problems" but could possibly be modified into a "real repeal" of the ACA.

"I believe we can get it done," Cruz said. "I can tell you, the last week, four days, I've been at the White House meeting with the president, with the vice president, saying, 'We've got to get it done.' "

Various changes have been floated since the bill was unveiled this month. Conservatives have pushed for an earlier phaseout of the ACA's Medicaid expansion, moving it from the end of 2019 to the beginning of 2018, but GOP moderates in the House and Senate have pushed back on that notion.

"Doing that would be a nonstarter and would be enormously and hugely problematic for many of our members," said Rep. Charlie Dent (R-Pa.), a co-chairman of the centrist Tuesday Group.

Meadows said Wednesday that the Freedom Caucus is closely focused on repealing more of the ACA's mandates governing the extent of insurance coverage. "That is probably the No. 1 priority," he said. "If we can get those, it would make the rest of it a whole lot easier."

GOP leaders, however, have kept those provisions out of the pending legislation, arguing that their inclusion could threaten the bill's passage in the Senate and that many of those mandates can be undone through Trump administration actions.

In another sign of the effect of the CBO report, Sen. John Thune (R-S.D.) floated a proposal to recalibrate the tax credits established under the House bill to offer more substantial help to low-income Americans. The House bill would offer assistance to individuals making as much as $115,000 a year; Thune's amendment would phase out aid for those making about $75,000 or more.

"We want to build on what the House has done, and we think that this amendment does that," Thune said. "It just makes it more defensible both in terms of the policy implications and the politics."

Kelsey Snell, Sean Sullivan, Elise Viebeck and David Weigel contributed to this report.