Republican opponents of President Barack Obama’s signature domestic achievement accused Democrats of back-room deal making, rushed legislating and strong-arm partisan tactics, even as the health care bill plodded toward passage over months of deliberation and public debate.
But wheeling and dealing may be what the Republican leaders need to get the health bill through the House as they dash toward a vote as early as Thursday. The House leaders released a set of revisions to the bill late Monday night, including some to speed up the repeal of taxes in the Affordable Care Act.
The newly released set of changes does not directly provide more generous tax credits for older Americans, as many Republicans had been requesting, but it lays the groundwork for the Senate to enhance those tax credits at a later stage in the legislative process.
“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,” the House speaker, Paul D. Ryan, said in a statement.
President Trump and House conservatives already agreed to other changes involving Medicaid, including offering states the option of imposing a work requirement for certain able-bodied beneficiaries. They also agreed to let states choose a lump-sum block grant to fund their Medicaid programs instead of a per-capita allotment originally set in the House bill.
The changes designed to win over conservatives may still not secure the votes of some of the most hard-line among them, including many members of the House Freedom Caucus. But in a big break for Mr. Trump and Mr. Ryan, the group’s leader, Representative Mark Meadows of North Carolina, said it would not take a collective position on the bill.
That gave Mr. Trump the power to woo members one by one. The president planned to meet with House Republicans at the Capitol on Tuesday.
But House leaders also faced a problem from the other direction: Some Republicans had misgivings about the House bill not because they viewed it as “Obamacare Lite,” but because they worried that it would cause millions of people to lose health insurance or would inflict great harm on their districts.
By offering a provision to please Republicans from New York — which expanded Medicaid under the Affordable Care Act — House leaders could stand to secure several needed votes, with little risk of alienating other members.
Representative John J. Faso, Republican of New York, said the state would be provided a substantial period of time to prepare for the change.
“The New York State property tax burden is one of the worst in the country, and Medicaid is part of the reason,” Mr. Faso said.
Mr. Faso and his fellow Republicans from New York had leverage. Representative Chris Collins, who pushed for the provision with Mr. Faso, noted that House leadership “was concerned about getting the votes” to get the health bill passed.
“I suggested we put this in,” Mr. Collins said, “and the question that came back was, ‘If we do it, can we get the New York votes?’” He said aside from one member, “the rest of us, kind of as a pack, went to leadership and said, ‘Yeah, you get this in here, you’ve got our votes.’”
Mr. Collins, a former Erie County executive, said he now believed that eight of the nine Republican members of New York’s House delegation would vote for the bill. “If they did not have the New Yorkers, I’m not sure they could get it over the finish line,” he said.
Mr. Cuomo, who had already warned that the House bill would cause New York to lose billions of dollars, said the change sought by the Republicans would have dire consequences.
“The cut is so severe that the majority of hospitals, nursing homes and assisted living facilities located in upstate New York and on Long Island would be devastated,” Mr. Cuomo said.
Medicaid, which provides health care to low-income people, is jointly financed by the federal government and the states. New York raises some of its share from counties, which have long chafed under what they view as an “unfunded mandate” from Albany.
County property taxes represent only a portion of the overall amount of property taxes that are paid by New Yorkers. A much larger share goes toward schools.
But William Cherry, the Schoharie County treasurer, said upstate counties would be able to make a significant reduction to their property taxes if they did not have to shoulder part of the cost of the state’s Medicaid program.
“This would be a huge step and a great benefit to taxpayers,” said Mr. Cherry, a Republican who is president of the New York State Association of Counties.
The provision being added to the House bill would not apply to New York City, which would continue to foot the bill for its share of Medicaid costs.
Kenneth E. Raske, the president of the Greater New York Hospital Association, said the provision would be harmful to hospitals and Medicaid beneficiaries.
“Rather than providing relief for county taxpayers,” Mr. Raske said, “the state would surely respond to the lack of federal revenue through huge spending cuts,” and those cuts could pose a risk to hospitals and their patients.
Bea Grause, the president of the Healthcare Association of New York State, said the provision being added to the House bill might give “the appearance of tax relief,” but would really just amount to shifting costs from counties to the state, while still leaving patients in need of care.
She, too, warned of a devastating effect on hospitals in New York. “It adds insult to injury,” she said.