In 2014, a family with two adults and two or more children, for example, would pay $285 or 1 percent of the family’s income over the $20,300 filing threshold, whichever is greater; those jump to $2,085 or 2.5 percent by 2016 and rise with inflation after that.

For instance, a family of four making $59,000 a year could face a choice between a $387 penalty the first year or, in a typical “silver” or midpriced policy offered on the California exchange, a premium of nearly $4,800 after the federal subsidy, with a $4,000 deductible, according to the Kaiser Family Foundation subsidy calculator. There is variation from plan to plan, but the deductible typically would not apply to doctor visits, preventive care, lab tests or generic drugs, although some regular co-payments would apply.

“Are they going to buy it?” said Robert Laszewski, president of Health Policy and Strategy Associates, a health care industry consultant in Alexandria, Va. “I don’t mean this as an attack on Obamacare. I think it’s a difficult political problem.”

The federal website, which serves residents of 36 states, appears to acknowledge this problem in a not-quite-threatening way: “If someone who can afford health insurance doesn’t have coverage in 2014, they may have to pay a fee. They also have to pay for all of their health care.”

The penalty, despite its unpopularity, is the glue that holds the Affordable Care Act together. Unless people are forced to buy insurance, health policy experts say, young and healthy people may stay away, leaving only the more expensive patients in the plans, which will quickly drive up premiums. And it was the penalty that the United States Supreme Court relied on to uphold the individual mandate, reasoning that it was a legal use of Congress’s taxing authority.

The sotto-voce treatment of the penalty resembles the strategy Massachusetts used when it set up its universal health insurance program several years ago. It took a sales approach at first, using the Red Sox in its campaign to appeal to men, who tend to be a little more resentful of being pushed into something, said Jon Kingsdale, the executive director for the first four years.

In November 2007, with barely two months left to sign up, his state began emphasizing the penalty, and volume soared, he said. “That was very effective as a call to action,” Mr. Kingsdale said.