The Obama administration has taken a hard line with governors about an option to expand Medicaid under the new health law, telling them to take it or leave it — but leave it and lose access to millions of federal dollars.

It turns out there is some wiggle room after all.

In an unexpected move, Health and Human Services Secretary Kathleen Sebelius recently agreed to a proposal by Arkansas Gov. Mike Beebe (D) to reject the Medicaid expansion and instead use federal money to buy private health insurance for the 200,000 people who would have been covered under the expansion.

That kind of arrangement could be appealing for other states in which expanding Medicaid, the health program for the poor and disabled, has been politically unpopular.

HHS officials have indicated other states might be permitted to use a similar strategy.

“We’re exploring avenues in which that might be able to happen,” said Gary Cohen, director of HHS’s Center for Consumer Information and Insurance Oversight, in a conference call with reporters Thursday.

Details of the Arkansas plan have yet to be finalized or agreed to by the state legislature. Still, the possibility that states can go a third route, rather than accepting or rejecting the Medicaid expansion outright, has thrown an element of uncertainty into the politically charged atmosphere surrounding the 2010 health-care law, which will extend health coverage to millions of uninsured Americans next year.

But it has also perplexed some experts who say the Arkansas move, if adopted by other states, could be vastly more expensive for the government.

According to Congressional Budget Office estimates, it will cost about $9,000 to buy a person private insurance on the health insurance exchanges created by the law, compared with about $6,000 to add the person to Medicaid.

“This is the feds committing themselves to paying much more, which doesn’t make a whole lot of sense,” said Leonardo D. Cuello, director of health reform for the nonprofit National Health Law Program.

Expanding Medicaid was a key pillar of the health law. States were called upon to open the program to anyone who earns up to 138 percent of the federal poverty level, which this year was $23,550 for a family of four. The federal government would pick up the entire tab for the 17 million new Medicaid recipients for three years.

Last year, the Supreme Court ruled that the federal government could not compel states to expand Medicaid under the law, leading some Republican governors to opt out. But some of the law’s sharpest critics, such as New Jersey Gov. Chris Christie (R), are going along with it because of pressure from advocates and to avoid walking away from millions of federal dollars.

Nationally, 26 states and the District have expressed a desire to expand Medicaid, according to the nonpartisan Kaiser Family Foundation. Seventeen have said they will reject it, while seven are weighing their options.

Federal health officials say they have yet to see a concrete proposal from Arkansas or to assess the cost implications. But they said the idea of using Medicaid dollars to buy private insurance isn’t new. And they have long encouraged flexibility on the part of states when it comes to the Medicaid expansion.

“Our goal in our work with states has been to be as flexible as possible within the confines of the law,” Erin Shields Britt, a spokeswoman for HHS, said in a statement. “In her meeting with Governor Beebe, Secretary Sebelius expressed support for ideas from the state that would take advantage of this flexibility and said she was glad to see the state considering an innovative, state-based approach.”

States on both sides of the Medicaid issue may reassess their choice in light of the decision on Arkansas, said Sara Rosenbaum, a health law professor at George Washington University.

Conservative states might find buying coverage from private insurers more palatable than expanding a government program. Even Democratic-led states might prefer this arrangement because it eliminates some bureaucratic hurdles.

“If Arkansas is allowed to do this, I expect it to spread like wildfire,” Rosenbaum said.

Arkansas officials argue the move could ultimately save money, in administrative charges and if other measures are taken to control the cost of health care. They say it would have been difficult, if not impossible, to persuade the Republican-controlled legislature to expand Medicaid and that, from an ideological standpoint, using private insurance is more appealing to lawmakers from both parties.

“There’s the feeling around here that if the private market can do something . . . we ought to let them and not create a larger government program,” said John Selig, director of the Arkansas Department of Human Services. “We feel like this is a very good deal.”

Sarah Kliff contributed to this report.