LITTLE ROCK, Ark. — Last year, the Republicans who control this state’s Legislature devised a politically palatable way to expand Medicaid under President Obama’s health care law. They won permission to use federal expansion funds to buy private insurance for as many as 250,000 poor people instead of adding them to traditional Medicaid, which conservatives disparage as a broken entitlement program.

But just as the idea is catching fire in other states with Republican or divided leadership — Iowa has adopted a version of the plan, and New Hampshire, Pennsylvania, Utah and other states are exploring similar avenues — Arkansas may abruptly reverse course, potentially leaving the 83,000 people who have signed up so far without insurance as soon as July 1.

Facing pressure from conservative challengers in the May primary, several Republicans who supported the plan last year are now considering switching their vote when the Legislature votes to reauthorize its financing, possibly as soon as next week. The defection of just one Republican could kill the program, state officials said.

“You’ve got a very small minority of people who can derail this,” said Gov. Mike Beebe, a Democrat who helped engineer the plan but will leave office at the end of the year because of term limits. He warned that ending the program would create an $85 million hole in his proposed budget — and devastate hospitals that were counting on the new federal funds.