Prompt enrollment is urgent for people in several circumstances. Some have no coverage, either because they haven’t been able to afford it or, like Momi, because they have pre-existing medical issues that led insurers to reject them in the past. Some have insurance that is going to expire. That group includes people whose health plans have been canceled and those in a high-risk pool that is closing. For people with serious medical issues, such as cancer patients in the middle of treatment, the loss of coverage could be medically and financially devastating.

Sara Collins, a vice president at the Commonwealth Fund, a New York health care foundation, predicts two waves of people will try to sign up for plans in the first half of December: those who had tried to shop on the websites but were stymied by technological glitches and those who were able to look at plans but didn’t settle on one.

For those who wait until the Dec. 23 deadline — either by choice or because they encountered difficulties—insurers will have just a week to process the applications before people can start filing claims. Robert Laszewski, an insurance industry consultant, says insurers generally need two weeks to add newly covered people into their computer systems. “The chances are we’re going to see lots of customer service problems,” he says.