FILE - In this Dec. 21, 2016, file photo, Wisconsin Gov. Scott Walker speaks during an interview with The Associated Press in Maple Bluff, Wis. Republican governors who turned down billions in federal dollars from an expansion of Medicaid under President Barack Obama’s health care law now have their hands out in hopes the GOP Congress comes up with a new formula to provide insurance for low-income Americans. (AP Photo/Scott Bauer, file)

DES MOINES, Iowa (AP) — Republican governors who turned down billions in federal dollars from an expansion of Medicaid under President Barack Obama's health care law now have their hands out in hopes the GOP-controlled Congress comes up with a new formula to provide insurance for low-income Americans.

The other GOP governors, such as Ohio Gov. John Kasich, who agreed to expand state-run services in exchange for federal help — more than a dozen out of the 31 states — are adamant that Congress maintain the financing that has allowed them to add millions of low-income people to the health insurance rolls.

These two groups of Republicans embody the difficulty the emboldened GOP congressional majorities face: Make good on their promises to repeal the 2010 health care law while preserving popular provisions.

With Congress starting to consider plans for annulling and reshaping Obama's overhaul, Republican governors and lieutenant governors from 10 states met privately for more than two hours Thursday with GOP members of the Senate Finance Committee and raised concerns about how lawmakers will reshape Medicaid.

"They're worried about how it all works out," Finance panel chairman Orrin Hatch, R-Utah, said after the session in a Senate office building.

GOP senators and governors stressed the need for giving states more flexibility to shape their Medicaid programs. That's a change that worries Democrats, who say some states would inevitably end up covering fewer people or offering skimpier benefits.

Arkansas Gov. Asa Hutchinson said governors could find savings by being allowed to impose "work incentives" for some beneficiaries. Kasich suggested shifting people who earn just above the poverty level from Medicaid to the online exchanges that Obama's law created for buying coverage.

"I think they understand this is not simple and I think they know they have to get it right," Kasich said.

A chief worry by governors was whether states that accepted extra federal money to expand Medicaid to more people would lose that extended coverage. Sen. John Cornyn, R-Texas, said afterward that "it ain't going to happen," though he did not detail how.

In a letter he carried to Capitol Hill, Kasich warned that repealing Obama's law without an alternative in place could interrupt health care coverage for hundreds of thousands in Ohio and urged he "be granted the flexibility to retain the adult Medicaid coverage expansion." Ohio has added roughly 700,000 recipients to the program since the law took effect in 2013.

Unlike Kasich, 19 Republican governors successfully defied the Affordable Care Act's mandate that states open up Medicaid to more people.

It was a major expansion of the state-federal health insurance system whose primary purpose has grown in its 52 years from backstop medical assistance for the poor to the go-to program for closing gaps in private health insurance system.

In the three years since the Affordable Care Act went into effect, Medicaid enrollment has grown by about 18 million people, to roughly 75 million, according to the federal Centers for Medicare and Medicaid Services.

Wisconsin Gov. Scott Walker notably turned down more than $500 million for his state. Determined to win over conservative voters for his presidential bid, he doubted the federal government would keep its word to cover 100 percent of expansion costs in the first three years, and 90 percent over the long term.

On average, the federal government's contribution accounts for 56 percent of a state's Medicaid budget, making the financing terms under the health care law much more generous.

Republicans have long sought block grants or lump-sum payments for health care. The money has helped them maintain their budgets, while the relative lack of heavy regulation has allowed governors freedom to experiment with social services policy.

But with Republicans, backed by President-elect Donald Trump, pursuing repeal of the law, Walker and others GOP governors are asking specifically for the Medicaid money, and fewer rules for spending it.

"Now that Barack Obama is no longer going to be at the White House, it is going to be much more palatable for Republican governors to seek additional funding," said Ron Pollack of Families USA, a leading advocate for Obama's law.

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