It is people like Eric Richter and his wife, Dani — uninsured and living in the unstable space between poverty and the middle class — that the law was intended to help. They earned too much to qualify for government-sponsored health care, but worked in jobs that did not come with health benefits.

Under the law, about half the newly insured would be covered by Medicaid, which would extend to individuals earning less than $15,400. The other half, the working poor, individuals with incomes up to $44,600, would receive subsidies.

According to a subsidy calculator provided by the Kaiser Family Foundation, the Richters’ insurance premium would be $165 a month under the new law, a sum they said they would eagerly pay. The small stone drilling firm where Mr. Richter works offers no health coverage, and the family could not afford the more than $600 a month it would have cost to buy it on their own.

“It’s hard to pay for the unknown, when you’re struggling to cover the known,” said Mr. Richter, who is 39. “I know it sounds irresponsible, but that’s just the way it was. It’s a game of roulette you hope you’re going to win.”

After he got the tumor on his leg, the couple said, Mr. Richter tried to better his odds. He cut out sugar and ate beets he grew in his garden because he heard that might help. But the bump kept growing. His wife sewed him special pants to accommodate its size, as big as a melon. He started standing in church. Driving was excruciating.

When they found he had cancer, the family struggled with how they would pay for his care. Once he was turned away from a scan because he did not have insurance. Eventually a doctor took him under his wing, and insisted he be treated.

In late May, Mr. Richter had surgery. He is waiting for the bill. He has not been able to work as he recuperates.