WASHINGTON >> Trying to head off a new round of consumer headaches with President Barack Obama’s health care law, the insurance industry said Tuesday it will give customers more time to pay their premiums for January.

America’s Health Insurance Plans, the main industry trade group, says the voluntary steps include a commitment to promptly refund any overpayments by consumers who switched plans and may have gotten double-billed by mistake.

Though the HealthCare.gov website is working far better this year, the industry announcement highlights behind-the-scenes technical issues between the government and insurers that have proven difficult to resolve. Last year’s enrollment files were riddled with errors, and fixing those has been a painstaking process. As a result, renewing millions of current customers is not as easy as it might seem.

The industry “wants to do everything we can to make sure consumers have greater peace of mind about their health care coverage and support them throughout the open enrollment process,” Karen Ignagni, head of the trade group, said in a statement.

The health care law offers subsidized private insurance to people who don’t have a health plan on the job. Renewing coverage each year is standard operating procedure for the industry, but 2015 is the first renewal year for the health law. The process involves a massive electronic data transfer from the government to insurers, happening right around the holidays. Insurers then have to use that data to generate new cards for their customers.

Normally, premiums for January would be due by Dec. 31. The industry’s grace period for 2015 could vary among different carriers, so consumers should check with their plan. Insurers say they also plan to help customers who have problems filling prescriptions or getting medical care at the start of the year.

Midnight Monday, Pacific time, was the deadline for new customers in most states to pick a health plan to take effect Jan. 1. It was also the deadline for current enrollees to make changes that could reduce premium increases before the new year. The administration announced a last-minute extension for some people unable to get through to the jammed federal call center.

Making matters more confusing, open enrollment actually runs for another two months, until Feb. 15. People enrolling by that date will get coverage starting March 1. Current customers can still make plan changes through Feb. 15.

Based on early numbers, it’s looking like the majority of the roughly 6.7 million current customers have opted to stay with the plans they have now and be automatically renewed Jan. 1.

Assuring that happens as smoothly as it’s been advertised is the administration’s next major challenge. The insurance industry announcement provides a safety valve for the administration. It mirrors similar steps the industry took last year to soften the consequences of the botched rollout of health insurance markets around the country.

The favorite political scapegoat of the White House during the battle to pass the health care law, insurers keen on signing up millions of new taxpayer-subsidized customers have turned into indispensable allies.