(Bloomberg) — The Obama administration is considering adding an extra Patient Protection and Affordable Care Act (PPACA) coverage enrollment period for tax filers who learn they owe a fine for not carrying insurance last year, to give them a chance to avoid even heavier penalties in 2015.

“You’re going to hear from us, one way or another, within the next two weeks on whether that’s something that we would do,” Health and Human Services (HHS) Secretary Sylvia Mathews Burwell said Friday. “It’s an issue that’s been raised.”

She talked about the coverage enrollment deadline in an interview in Austin, Texas, where she’s traveling to promote PPACA public exchange insurance plans.

The open enrollment period for 2015 started Nov. 15 and is set to end Sunday in most of the country.

See also: Lawmakers’ exchange pans enrollment proposal.

A new enrollment period would let people sign up as soon as they get a taste of the financial penalty that comes with not enrolling. Americans who didn’t have insurance in 2014 may owe a fine of as much as 1 percent of their income. If they remain uncovered this year, the fine may as much as double, to 2 percent of their income. Income tax filings are due April 15.

The Treasury Department has estimated as many as 6 million people may owe the penalty for not carrying insurance in 2014. At press time, about 10 million people had signed up for insurance for 2015 through the PPACA exchange system. Many more had coverage through employers or through public programs, or had purchased individual coverage outside the public exchange system.

Elizabeth Colvin, director of Insure Central Texas, a local advocacy group, asked Burwell about an extra enrollment period in a meeting earlier in the day.

“It needs to happen,” she said in an interview. “People who are penalized on April 15 can’t do anything.”

In California, KQED is reporting that managers of the state-based Covered California exchange are considering letting consumers who start an application by Sunday finish it as late as Friday, and that they also are considering providing enrollment access for consumers who learn about the PPACA tax penalty system after Feb. 15.