WASHINGTON — House Republican leaders, trying to lock down the votes of wavering upstate New York Republicans, inserted a last-minute special provision in their health care bill that would shift Medicaid costs from New York’s counties to its state government.
The move — one of a number of late changes designed to gain more votes — would affect New York State only. It could save county governments outside of New York City $2.3 billion a year. But it could shift costs to state taxpayers or deny New York that same total in matching federal aid if the state continues to require those counties to contribute to the cost of Medicaid. Upstate New York Republicans, backed by local government officials, pressed for the measure over the angry opposition of New York’s Democratic governor, Andrew M. Cuomo.
“The more we learn about the repeal and replacement for the Affordable Care Act, the sicker New York gets,” Mr. Cuomo said in a statement Monday night.
Republican leaders were in no position to oppose the demands of back-bench House members as they scrounged for a majority of votes. Democrats used such targeted provisions to push the Affordable Care Act over the finish line in 2010 — to the angry cries of Republicans who accused them of kickbacks and buyoffs.
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 were to release a final set of revisions to the bill Monday night.
President Trump and House conservatives already agreed to other changes involving Medicaid, including offering states the option of imposing a work requirement for 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.
For more moderate members, leaders plan to make tax credits more generous for older Americans to help them purchase insurance policies on the free market.
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 House Speaker Paul D. 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 when he meets with them at the Capitol on Tuesday morning.
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 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. 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 — much of which goes toward paying for schools.
But William Cherry, the treasurer in Schoharie County, said upstate counties would be able to make a significant reduction to their property taxes if they did not have to foot part of the bill for 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 affect New York City.
Kenneth E. Raske, the president of the Greater New York Hospital Association, said the amendment 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.