WASHINGTON — House Republican leaders, racing toward a planned vote Thursday on their proposed health-care overhaul, unveiled changes to the legislation late Monday that they think will win over enough members to secure its passage.

The tweaks addressed numerous Republicans’ concerns about the legislation, ranging from the flexibility it would give states to administer their Medicaid programs to the amount of aid it would offer older Americans to buy insurance. They are the product of two weeks of negotiations that stretched from the Capitol to the White House to President Trump’s Florida resort.

The bill’s proponents also appeared to overcome a major obstacle Monday after a key group of hard-line conservatives declined to take a formal position against the bill, known as the American Health Care Act.

The House Freedom Caucus has threatened for weeks to tank the legislation drafted by House Speaker Paul Ryan, R-Wis., arguing that it does not do enough to undo the seven-year-old Affordable Care Act. Their neutrality gives the legislation a better chance of passage: If the group of about three dozen hard-right Republican members uniformly opposed the bill, it could block its passage.

Their decision not to act as a bloc frees House leaders and White House officials to persuade individual Freedom Caucus members to support the measure – a process that the Freedom Caucus’s chairman said was underway.

“They’re already whipping with a whip that’s about 10 feet long and five feet wide,” said Rep. Mark Meadows, R-N.C. “I’m trying to let my members vote the way that their constituents would want them to vote. … I think they’re all very aware of the political advantages and disadvantages.”

House leaders hope to pass the bill Thursday and then send it to the Senate. Trump is expected to press for the bill’s passage in a Tuesday morning meeting with Republican lawmakers.

Some of the changes unveiled Monday were made to placate conservatives, such as accelerating the expiration of the ACA’s taxes and further restricting the federal Medicaid program. But a major push was made to win moderate votes, including a maneuver that House leaders said would allow the Senate to beef up tax credits for older Americans who could see major increases in premiums under the Republican plan.

There were signs Monday that the bill had growing support among the moderate wing of the House. Republican Rep. Tom MacArthur, R-N.J., who had voted against the leadership in an early procedural vote on the health-care legislation, said that he was “satisfied enough that I will support the bill.”

MacArthur said he was assured that the bill would do more for older and disabled Americans covered under Medicaid and that an additional $85 billion in aid would be directed to those between ages 50 and 65.

“That’s a $150 billion change in this bill to help the poor and those who are up in years,” he said.

Several House Republicans from Upstate New York won an amendment that would allow counties in their state to keep hundreds of millions of dollars of local tax revenue that they forward to the state government to fund its Medicaid program. One member, Rep. Claudia Tenney, R-N.Y., told the Syracuse Post-Standard on Monday that her support of the bill was conditioned on the amendment’s inclusion.

Opponents of the bill – Republicans and Democrats alike – called the deal a sordid giveaway on social media networks Monday night. Many compared it to the state-specific deals that were cut to pass the Affordable Care Act in 2009 and 2010 and panned by Republicans – such as the Medicaid reimbursement boost that then-Sen. Ben Nelson, D-Neb., secured for his home state that Republicans mocked as the “Cornhusker Kickback.”

The Freedom Caucus had pushed for a variety of alterations, from an earlier phaseout of the ACA’s Medicaid expansion to a more thorough rollback of the insurance mandates established under the law. But for political and procedural reasons, few of the group’s major demands stand to be incorporated into the bill.

“It’s very clear that the negotiations are over,” said Meadows, who met with White House officials at Trump’s Mar-a-Lago resort in Florida on Saturday.

Many Freedom Caucus members who left the group’s Capitol Hill meeting Monday night said they remained sharply opposed to the legislation.

“Nothing’s changed,” said Rep. Jim Jordan, R-Ohio, a co-founder of the caucus. “We’ve still got lots of problems with this bill. … The president’s a good man, and the White House has been great to work with, but opposition is still strong with our group.”

Under the group’s rules, it can take a formal position to oppose the bill if 80 percent of its members agree. No Democrats are expected to support the bill, meaning Republican leaders can afford to lose no more than 21 of their own members.

Meadows said after Monday night’s meeting that taking a hard position against the bill “creates some dynamics within the group that perhaps we don’t want to create,” hinting at tensions in the group’s ranks. One of its members, Rep. Gary Palmer, R-Ala., decided to support the bill last week when he met with Trump in the Oval Office, emboldening House leaders who think that even hard-liners will be hard-pressed to oppose Trump.

“This is a defining moment for our nation, but it’s also a defining moment for the Freedom Caucus,” Meadows said. “There are core things within this bill as it currently stands that would violate some of the principles of the Freedom Caucus.”

Attending the Freedom Caucus meeting Monday were three senators opposed to the House bill – Ted Cruz, R-Texas, Mike Lee, R-Utah, and Rand Paul, R-Ky., – who hold leverage to block the bill in their own chamber, where Republicans hold a two-seat majority. Cruz said he told the House members that the leadership strategy of pursuing distinct “phases” of legislation was a dead end and that they needed to push for changes in the present bill.

“The Senate Democrats are engaging in absolute opposition and obstruction, and it is difficult to see that changing anytime soon,” Cruz told reporters after leaving the meeting.

Trump’s visit to the Hill on Tuesday signals that GOP leaders and the president consider larger-scale talks with key blocs of House members to be essentially complete. The effort now turns toward persuading individual members to vote for the package.

Ryan credited Trump’s backing in a statement Monday: “With the president’s leadership and support for this historic legislation, we are now one step closer to keeping our promise to the American people and ending the Obamacare nightmare.”

Trump’s visit Tuesday will be his first appearance at the weekly House Republican Conference meeting since becoming president. He last privately addressed Republican lawmakers as a group at the party’s policy retreat in Philadelphia in late January and has met with small groups of members on several occasions since.

Trump won the backing of Palmer and several other conservative House members Friday when he agreed to make changes to the Medicaid portion of the bill, including giving states the option of instituting a work requirement for childless, able-bodied adults who receive the benefit. Those changes were included in the leadership-backed amendments that will be incorporated into the bill before it comes to a final vote.

To address concerns expressed by a broader swath of Republican lawmakers – conservatives and moderates alike – leaders said they hoped to change the bill to give older Americans more assistance to buy insurance.

In an extreme case laid out in a Congressional Budget Office analysis of the bill, a 64-year-old earning $26,500 a year would see yearly premiums rise from $1,700 under the ACA to $14,600 under the Republican plan.

House leaders said they intended to provide another $85 billion of aid to those between ages 50 and 64, but the amendment unveiled late Monday did not do so directly. Instead, the leaders said, it “provides the Senate flexibility to potentially enhance the tax credit” for the older cohort by adjusting an unrelated tax deduction.

That workaround, aides said, was done to ensure that the House bill would comply with Senate budget rules and to ensure that the CBO could release an updated analysis of the legislation before the Thursday vote.

But it also means that the House members who pushed for the new aid will have to trust the Senate to carry out their wishes.