JEFFERSON CITY, Mo. (AP) — Given the choice of whether to expand Medicaid under President Barack Obama’s health care law, many Republican governors and lawmakers initially responded with an emphatic “no.”

Now they are increasingly hedging their objections.

A new “no, but …” approach is spreading among GOP states in which officials are still publicly condemning the Democratic president’s Medicaid expansion yet floating alternatives that could provide health coverage to millions of low-income adults while potentially tapping into billions of federal dollars that are to start flowing in 2014.

The Medicaid health care program for poor, which is jointly funded by the federal and state governments, already covers about one in five people in the U.S. Expanding it was the way Obama envisioned covering many more low-income workers who don’t have insurance. The new Republican alternatives being proposed in states generally would go part of the way, but cover fewer people than Obama’s plan, guarantee less financial help or rely more on private insurers.

But so far, many of the Republican ideas are still more wistful than substantive. It’s uncertain whether they will actually pass. And even if they do, there’s no guarantee Obama’s administration will allow states to deviate too greatly from the parameters of the Affordable Care Act while still reaping its lucrative funding. Yet a recent signal from federal officials that Arkansas might be able to use Medicaid money to buy private insurance policies has encouraged Republicans to try alternatives.

The GOP proposals could lead to another health care showdown between the White House and states, leaving millions of Americans who lack insurance waiting longer for resolution. Officials in about 30 states that are home to more than 25 million uninsured residents remain either defiant or undecided about implementing Obama’s Medicaid expansion, according to an Associated Press survey.

Supporters of the Medicaid expansion have built coalitions of hospitals, businesses groups, religious leaders and advocates for the poor to try to persuade reluctant Republicans of the economic and moral merits of Obama’s health care plan. But some Republicans believe the pressure ultimately will fall on Obama to accept their alternatives if he wants to avoid a patchwork system for his signature accomplishment.

“If the Obama administration is serious about innovative ways to bring down the cost of health care, it’s going to cooperate with conservative ideas rather than continue down its one-size-fits-all, far-left-wing ideological path,” said Missouri Rep. Jay Barnes, a Republican from Jefferson City.

A House committee led by Barnes already has defeated Obama’s version of Medicaid expansion. It is to hear public testimony Monday on his “market-based Medicaid” alternative that would award health care contracts to competing private insurers and provide cash incentives to patients who hold down their health-care costs. His proposal would contain costs by covering fewer children than Medicaid now does and adding fewer adults than Obama’s plan envisions.

Committees in Florida’s Republican-led Legislature also have rejected a Medicaid expansion for roughly 1 million of the state’s poorest residents, even though it is backed by GOP Gov. Rick Scott. Now Republican Sen. Joe Negron is pursuing an alternative that would use federal funds to provide vouchers for low-income residents to buy private policies. Negron said he still doesn’t believe expanding Medicaid is the right decision, but he wants to help Florida residents get health coverage.

“We don’t want to do it the Washington way. We want to do it the Florida way,” Negron said.

Republican Ohio Gov. John Kasich also has been in discussions with the Obama administration about providing subsidized insurance instead of full Medicaid coverage for more adults. Republican governors in Texas, Nebraska and Indiana want the federal government to award Medicaid money as block grants to states.

“It’s a two-step for many of these Republican governors. When they look at the numbers they want to do it, but they want to distance themselves from Obamacare at the same time,” said Drew Altman, president of the Kaiser Family Foundation, a nonprofit that analyzes health care policies.

That might be fine with the Obama administration.

“There actually is quite a bit of flexibility on how they can approach this, and the federal government has indicated they want to get to ‘yes’ “ said Joan Alker, co-executive director of Georgetown University’s Center for Children and Families in Washington, D.C.

As originally enacted, the Affordable Care Act required states to expand Medicaid to adults earning up to 138 percent of the federal poverty level, about $32,500 annually for a family of four. A Supreme Court decision last summer made the expansion optional for states but kept in place a powerful financial incentive.

The federal government will fully fund the expansion for the first three years, with the states’ share gradually increasing to 10 percent by 2020.

Health and Human Services Secretary Kathleen Sebelius said in December that getting full funding will still require a full expansion. Yet some Republicans in Missouri, South Dakota and elsewhere claim to see room for compromise.

LaTonya Jenkins, a 51-year-old laid off teacher’s aide who lives in temporary housing for the homeless in Kansas City, recently enrolled in Medicaid but could lose coverage if her part-time job pushes her income over Missouri’s strict eligibility limits. She recently traveled to Missouri Capitol to urge lawmakers to expand Medicaid.

“If they don’t, and they cut it out, then what are we to do? We’ll be lost,” said a tearful Jenkins, who has diabetes and cares for her grandson. “I’ll be sicker than ever and back in the hospital.”

–Email [email protected] and follow us @TheATRegister

• DAVID A. LIEB, Associated Press