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WASHINGTON (AP) — Several million people hit with new federal fines for going without health insurance will get a second chance to sign up starting Sunday, and that could ease the sting of rising penalties for being uninsured.

But as the enrollment window reopens, it's unclear how many know about the time-limited opportunity, let alone will take advantage of it.

Fines payable to the IRS are the stick behind the offer of taxpayer-subsidized private insurance under President Barack Obama's health care law. Virtually everyone in the country is now required to have coverage through an employer or a government program, or by buying individual policies.

This is the first year fines are being collected from uninsured people the government deems able to afford coverage. Tax preparation company H&R Block says the penalty averages about $170 among its affected customers. It usually is deducted from a person's tax refund.

Those penalized are mainly the kind of people the law was intended to help: low- and middle-income workers who do not have coverage on the job or are self-employed. Roughly 4 million people are expected to pay fines, according to congressional estimates. Many more will qualify for exemptions.

Travel agent Charles Baxter of Phoenix said his tax refund was reduced by $247 for being uninsured in 2014. He had not heard about the second chance to sign up for 2015 coverage.

Baxter says he will take another look now, but is not sure whether he will opt to buy insurance. Much of his income goes to help take care of his mother, who has health problems.

"I may have to see if any of the health care costs have changed, to where I might be able to squeeze it in, " he said. "But so far, it's not looking like it."

Baxter supports the overall goals of the health law, but says the government should also look at someone's expenses — not just income — before assessing the fine.

Penalties for being uninsured are going up this year, to a minimum of $325 for the full 12 months. That's a significant increase from the $95 minimum in 2014.

The new sign-up opportunity runs through April 30. To qualify, individuals have to certify to the government that they meet certain conditions, including:

—They did not know or understand that they were legally required to have coverage until after open enrollment officially ended Feb. 15.