But if the Trump administration allows Arkansas to scale back its Medicaid expansion population, some of the other 31 states that expanded the program will likely want to follow, as a way to save money and appease conservative legislators who think the Obamacare expansion went too far. Other states may be tempted to expand Medicaid, after holding back for years, if they can limit it to those earning at or below the poverty level. The federal government initially paid the full cost of the expansion, but now states are on the hook for 6 percent of the cost; their share will gradually grow to 10 percent over the next few years.

The Arkansas proposal would move about 60,000 people out of the program, by lowering the income threshold to the federal poverty level.

Mr. Hutchinson wants those earning between 100 and 138 percent of the poverty level to move to the Affordable Care Act marketplace, where they would get federal subsidies to buy private insurance. But that could end up costing the federal government more money — another reason the Trump administration may be slow to approve it. President Trump frequently refers to the marketplaces as “failing” and has taken a number of steps to weaken them.

Regardless, Mr. Hutchinson said Monday he was optimistic about winning approval to shrink the expansion population after meeting recently with Alex Azar, the new Health and Human Services secretary.

Mr. Hutchinson has long been under pressure from conservative Republicans in the Arkansas legislature who say the Medicaid expansion has proved too expensive, with far more people enrolling than originally estimated.

Arkansas is anticipating spending about $136 million in general revenue on its Medicaid expansion in the coming fiscal year, with the federal government spending an additional $2 billion. The state uses federal Medicaid funds to buy private insurance for the poor — an alternative that conservative Republicans found acceptable when it was first passed in 2013. About 285,000 people are now enrolled in the Medicaid expansion.

Cindy Gillespie, the director of the Arkansas Department of Human Services, said the state was planning to activate an online portal on March 30 where those subject to the requirement will be expected to record how they’re meeting it each month. In June, the state will start phasing it in, relying largely on its Department of Workforce services to connect job seekers with employment, education or training.