WASHINGTON — Consumers anxious over tight insurance deadlines and lingering computer problems during the holidays will get extra time to pay their premiums under President Barack Obama’s health care law, insurers announced Wednesday.

The board of the industry’s biggest trade group — America’s Health Insurance Plans — said consumers who select a plan by Dec. 23 will now have until Jan. 10 to pay their first month’s premium. That’s 10 extra days beyond a New Year’s Eve deadline set by the government.

The voluntary move comes as insurers and the government try to head off anticipated problems around the first of the year, when new coverage options for the uninsured take effect under Obama’s law, and when several million people whose existing policies were canceled must switch to new plans.

Expect even bigger political trouble for the president if consumers who made a good-faith effort to get covered through the government’s balky website show up at the pharmacy and can’t get prescriptions filled, or if they turn up in the emergency room and there’s no record that they are enrolled. The stakes would be higher this time because someone’s health could be jeopardized.

The administration applauded the industry decision. It will “ultimately make it easier for consumers to enroll” through the new online insurance markets, said Health and Human Services spokeswoman Joanne Peters. The federal HealthCare.gov website is now working reasonably well, but insurers still report accuracy problems with enrollment information the government is sending about their new customers.

Karen Ignagni, CEO of the industry group, said the decision was taken “to give consumers greater peace of mind about their health care coverage.” AHIP represents about 95 percent of the industry, including the major national carriers and nearly all the BlueCross BlueShield plans.

There may be a few insurers who do not follow the group’s lead, so consumers are advised to check with their carrier. Consumers must pay their first month’s premium on time for coverage to take effect.

The move burnishes the industry’s image and has no real downside, said Dan Mendelson, CEO of Avalare Health, a market analysis firm. “It’s useful for the consumer and not a problem for the plans,” he said.

Insurers will still get paid for January. “They can book the revenue, and they don’t need to worry about the cash flow,” Mendelson said.

But the announcement does more than grant extra time. It also reduces the risk that consumers switching plans could suffer an interruption in coverage because of the technology woes encountered by the federal sign-up system, and some state-run websites.

That’s particularly important for at least 4 million people whose existing individual plans were canceled because they did not meet standards under Obama’s law. Disruptions in coverage for those consumers could have major political consequences for Obama and beleaguered HHS Secretary Kathleen Sebelius.

Back in 2009, Obama had promised that people who liked their insurance would be able to keep it under his health overhaul plan. But that guarantee was shredded by the wave of cancellation notices, which crested right around the same time that HealthCare.gov was refusing to function for millions of potential customers. Obama’s poll ratings took a nosedive.

Under the industry announcement, consumers still must select a plan by Dec. 23 — next Monday.

But instead of having to pay their first month’s premium by New Year’s Eve, they now have until Jan. 10. That would let them have coverage retroactive to Jan. 1. Patients who get a pharmacy or medical bill during that period can later submit it to the insurance company for payment.

Insurers have complained that a significant number of the enrollments they have gotten from HealthCare.gov have problems that could prevent a consumer from getting covered on Jan. 1. That includes missing or incomplete information, duplicative entries and garble. The administration says its technical experts are aggressively tackling the problems, and that errors have been cut dramatically. But insurers say useless or corrupted files are still getting through. Government and industry are working together to clean up the records.

Without the extra time granted Wednesday, a consumer who paid in early January would have had to wait until Feb. 1 for coverage.