WASHINGTON (AP) ' Several million people hit with new federalfinesfor 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.Finespayable 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 yearfinesare 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 payfines, 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 thefine.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.They owed a penalty for being uninsured in 2014.Those requirements are for the 37 states served by the federal HealthCare.gov website. States running their own insurance exchanges may have different rules and deadlines. Penalties for 2014 are not refundable.The Obama administration acted after Democratic lawmakers raised concerns. With open enrollment officially over, someone who was uninsured and filed a tax return after Feb. 15 would not have been able to get coverage for 2015. That person would owe the penalty for 2014 and could get locked into a biggerfinefor 2015."Most people can assume that whatever they paid this year, next year they will pay twice that much or more," said Rep. Lloyd Doggett, D-Texas. "Why pay what is in essence a penalty, when you can be applying those dollars to protect your family'"The administration is publicizing the special sign-up period as tax filing season continues. For customers who paid afine, major tax preparation companies are notifying them about the second chance to get coverage.Tax preparers and some public policy experts have urged the government to move the health care law's sign-up period so it dovetails with tax-filing season. People expecting a refund might be willing to spend some of it on health insurance.Mark Ciaramitaro, vice president of health care services at H&R Block, said the penalty is definitely getting taxpayers' attention. "It's a surprise," he said. "For some people, it's having significant effects."Cari Gerrits of Atlanta was uninsured for part of last year when she was between jobs, and her penalty ended up being $191. She has coverage now through her job in marketing and business development for an engineering company."I'm supportive of having a baseline of care for everybody," she said. "But the marrying of a very complicated medical law with an already confusing tax law has probably not made it as popular as it could be."Jesse Bracewell of Huntsville, Alabama, was uninsured last year because he could not fit premiums into his budget as a college student finishing an engineering degree. He paid a penalty of $95. This year, he signed up to avoid risingfines."That penalty set me back about three weeks' worth of gas," Bracewell said.___Associated Press Social Media Editor Eric Carvin contributed to this report.Join the conversation about this storyNOW WATCH: A lawyer in Florida has come up with an ingenious way for drivers to evade drunken-driving checkpoints Click here to read full news..