Nationally, as many as about 20 percent of those who signed up for coverage that took effect in January have failed to pay their premiums on time, according to insurance companies and industry experts. Others may be keeping up with their premium costs but struggling to meet high deductibles, which many of the new plans have.

Mr. Elson is long divorced and lives alone but has an affectionate relationship with his daughter, who lives several states away. He carefully tends his backyard garden, jarring tomatoes and storing them on a shelf in his kitchen. Perhaps partly because of his advanced disease, he can be forgetful and disorganized: His home is strewn with alarm equipment, buckets of empty diet soda cans and unopened mail. In January, he said, he neglected to bill his customers who pay monthly.

“I plum forgot,” he said, shrugging.

His first premium payment was due March 8, for coverage that was to take effect March 1, and he missed the deadline. Several customers owed him money, he said, and after paying his rent, water bill and the fee for a car he had rented after his van broke down, he did not have enough money left for insurance.

He got some free diabetes medicine from Family Health Centers in February, but it was meant to last only a few weeks.

“That’s the next bill I’m paying,” he said. “You can trust me on that.”

Challenges for Providers

Family Health Centers has always been one of the few medical providers in Louisville to take all comers, regardless of their ability to pay, and it will not abandon that role in the Affordable Care Act era, said Mr. Wagner. Even last month, as a record percentage of its patients presented insurance cards, almost 30 percent of the medical appointments were still for “self-pay” customers with no coverage.

But already, the change in its patient mix is striking. The number of visits by Medicaid recipients last month was 30 percent higher than in February 2013. Visits by uninsured patients fell by 52 percent, to 1,760 from 3,697. Visits by patients with private insurance dropped slightly, but Mr. Wagner hopes they will rise as more people like Ms. Morse discover Family Health Centers and like what they find.

For now, the new revenue from Medicaid — which reimburses community health centers at a higher rate than private doctors — should help Family Health Centers erase a $2 million deficit in its $28 million budget, Mr. Wagner said.