The Kaiser analysis found the average penalty would be $661 per household for going uninsured in 2015 and $969 for 2016. For most people, the penalty comes out of their tax refund.

Mr. Murphy’s problem with the exchange plans is not affordability, he said. He could pay the $243 a month that the cheapest available plan would cost, and even the $6,750 annual deductible. It is more that he dislikes his options: all health maintenance organizations that do not allow customers to go out of their networks except in emergencies.

As for insurance policies sold outside the exchange, he did not explore them because, he said, “I just don’t see the point.”

“I’m just going on the hope that nothing bad is going to show up until I get a full-time position somewhere or there’s better choices,” he said.

For Tim Fescoe, a visual effects artist in Culver City, Calif., the problem with his health plan was that it seemed too bare-boned. That plan from Covered California, his state exchange, cost $455 a month for himself and his wife in 2014. But they dropped the plan, which had a $6,000 deductible for each spouse, and went uninsured last year.

“It literally covered zero medical expenses,” Mr. Fescoe said.

They are re-enrolling his wife, Wendy, 26, who may try to have a baby soon. But Mr. Fescoe, 37, said he was happier paying for doctors and drugs out of pocket than dealing with an insurance company.

“It would work better if everyone signed up,” he acknowledged. “But you’re asking a bunch of people to basically just give money into the system when they have an option not to.”