WASHINGTON — It’s crunch time to sign up for coverage under President Obama’s health care law. The website works much better now, but rising premiums and shaken faith among insurers have cast new shadows.

Tuesday is the deadline for millions of uninsured procrastinators to sign up in time for coverage to begin on Jan. 1. As the health insurance expansion enters its third year, their decisions are critical to its economic viability. A surge of younger, healthier customers could hold down premiums in a market that’s struggling to grow.

“Medical costs of enrollees have been higher than expected and total enrollment remains low,” said Caroline Pearson, a vice president at the consulting firm Avalere Health. “If participation is leveling off, then plans may be stuck with a risk pool that is not particularly balanced.”

More than half of the health law’s 23 nonprofit insurance cooperatives have folded, and even some major industry players have recently gone public with doubts.

There have been bumps with the health law, says business owner Rayna Collins of Lincoln, Nebraska, but overall she counts on it. She’s surprised, however, that many people she knows have remained uninsured.

“It’s heartbreaking to think that they could have affordable insurance,” said Collins. “They think it’s like going on welfare.” One friend believed incorrectly that insurers could still turn down customers with pre-existing health conditions, a practice barred under the law.

The Obama administration says it’s seeing a vigorous consumer response this sign-up season, with more than 1 million new customers already.

“All the evidence for us is that the marketplace is strong, it’s vibrant, and it’s growing,” said Andy Slavitt, head of the Centers for Medicare and Medicaid Services, which runs the government’s major insurance programs.

Still, the administration’s sign-up target for 2016, the president’s last full year in office, is modest: 10 million people enrolled and paying premiums at the end of the year, an increase of about 10 percent.

Tuesday is the deadline to sign up for coverage so it can take effect on the first of the year. It’s also the deadline to make any changes to existing coverage so they take effect Jan. 1. Current customers will be automatically renewed Jan. 1 if they make no changes, but they may save money now by shopping for a plan with lower premiums.

The fines for people who remain uninsured in 2016 have gone up substantially. A study from the nonpartisan Kaiser Family Foundation estimates that the average tax penalty will rise to $969 per household, or nearly 50 percent. Ahead of sign-up season, it was expected that premiums for health law plans would go up in most places. A wave of closures among the law’s nonprofit insurance co-ops led to more worries. But what really seems to have shaken confidence were recent comments by UnitedHealth CEO Stephen Hemsley that the nation’s largest insurer had made a bad decision in expanding into more of the law’s insurance exchanges.

Drew Altman, president of the Kaiser Foundation, says the health law’s insurance markets appear to be making progress. But they’re not there yet.

“It’s going to take more people enrolled to be fully successful,” Altman said.