A man looks over the Affordable Care Act signup page on the HealthCare.gov website. (Mike Segar /REUTERS)

The nation’s health insurance industry decided Wednesday to extend the deadline until Jan. 10 for Americans to pay for coverage that starts on New Year’s Day, as enrollment through the new federal and state insurance marketplaces appears to be surging.

After meager participation during the first two months, more than half a million people have chosen plans in the federal exchange since the beginning of December, according to government figures that have not been made public. Several states running their own exchanges are reporting sizable enrollment upswings, as well.

Just a few days remain before a Dec. 23 deadline to sign up for coverage that will begin Jan. 1, and the last-minute blitz that federal health officials have predicted appears to be materializing. It puts intense pressure on insurers to send bills to their new customers — and on consumers to pay right away.

Under government rules, coverage cannot begin until people pay their first month’s premium. Extending the payment deadline creates breathing room for the industry and for people who are eager for their insurance to begin, averting a holiday week in which tens of thousands of Americans might not know whether their coverage would start on time.

The extension does not change the Dec. 23 sign-up deadline. But the move suggests that private health insurance companies, whose leaders spent much of the fall griping about problems with the federal computer system HealthCare.gov, are entering a new phase in which they are worrying about how to handle an onrush of insurance-seekers.

The deadlines mark pivotal moments in the fate of the Affordable Care Act, a broad 2010 law intended to reshape health care in the United States, in part by slashing the ranks of the uninsured. As of Jan. 1, the day the new coverage will begin, most Americans will for the first time be required to have health insurance or risk a fine. The enrollment period for health plans in the federal marketplace began Oct. 1, but many people shopping for coverage were hampered by serious technical defects with the federal Web site, which Obama administration officials say has significantly improved.

The board of directors of America’s Health Insurance Plans, the industry’s main trade group, decided on the extension Wednesday. Its move goes beyond a time frame envisioned by the Obama administration, which last week directed insurers in the exchanges to give customers until New Year’s Eve to pay for health plans that start the next day.

Robert Zirkelbach, an AHIP spokesman, said that the trade group’s decision was not a response to the administration, but reflected the industry’s thinking. The organization is not compelling all its members to abide by the change, but all major insurers selling health plans through the new marketplaces already had agreed to do so, except in a few states, including Maryland, that set different deadlines.

The insurers were silent on several other kinds of flexibility that Health and Human Services Secretary Kathleen Sebelius asked the companies to provide. Those include allowing Americans who sign up in January to get coverage retroactive to the start of the month, and letting people stay on their current medicines — and, in certain instances, to keep their doctors — for the first month at no extra cost even if they are not part of their new coverage.

AHIP’s silence “is a clear indication the other requests may be problematic,” said an executive at a leading health plan in the South, who spoke on the condition of anonymity to avoid offending the administration. “There’s only so much that can plausibly be done, particularly on short notice.”

Insurers are sorting out rules for handling the increasing volume of customers. According to government figures, about 680,000 people had enrolled in plans through the federal insurance exchange as of earlier this week. That means that nearly 550,000 people signed up this month; figures released by the HHS show that about 137,000 people had chosen a health plan by the end of November.

Aaron Albright, a spokesman for HHS’s Centers for Medicare and Medicaid Services, which oversees the federal marketplace, declined to comment on the December figure. But he said, “We expect enrollment to increase given the technical improvements we’ve made to the site.”

The White House and its allies are continuing to urge Americans to get health coverage — and to tout the successes of several states among the 14 that are running their own marketplaces in which enrollment has been going smoothly. In a call with reporters organized by Families USA, a consumer health lobby, the directors of state exchanges said an average of 15,000 people per day were enrolling last week in California, 4,500 per day in New York and 1,400 per day in Connecticut.

In an event at the White House on Wednesday to spotlight health insurance for mothers, President Obama said that Mary Todd Glascock of Virginia Beach, Va. — whose 21-year-old son was able to stay on her insurance plan despite having a rare and aggressive cancer diagnosed two years ago — was among the people who will help promote the health-care law at the grass-roots level.

Standing with Todd and seven other mothers from along the East Coast, Obama said, “Nothing can replace the story that Mary Todd is telling in the grocery store to somebody who may be skeptical.”

Sarah Kliff and Juliet Eilperin contributed to this report.