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A person walks into the UniVista Insurance company office where people are signing up for health care plans under the Affordable Care Act, also known as Obamacare, on December 15, 2015 in Miami, Florida.
Joe Raedle—Getty Images

If you don't yet have health insurance coverage for 2016, pay attention: You must enroll in an Obamacare plan by Sunday, Jan. 31, or else you may have to go without insurance for the rest of the year—and you might be faced with a hefty tax penalty in 2017. Don't wait for an extension: Although some enrollees got a few extra weeks last year, the Obama administration says that won't happen this time around.

Under the Affordable Care Act, people who don't have health insurance have to pay a tax penalty unless they qualify for an exemption (more on that later). Most Americans don't have to worry about this because they get health coverage from an employer, Medicare, or another government program. But if you don't have coverage, you must buy private insurance. The Affordable Care Act created government-run exchanges, or marketplaces, where you can buy private plans, though you're also free to buy a plan from another broker.

If you make less than four times the poverty line—this year, that cut-off is $47,080 for an individual and $97,000 for a family of four—you'll qualify for a discount on your premiums in the form of a tax subsidy. So far this year, 83% of enrollees on the federal insurance marketplace, Healthcare.gov, qualified for a discount averaging $294 per person per month, according to the Department of Health and Human Services (HHS). On average, people who qualify for a subsidy pay $113 a month in premiums.

The catch? There's a limited window during which you're allowed to buy health insurance, and for 2016 it ends Jan. 31. Miss this deadline, and you may have to wait until next open enrollment period to buy coverage, which starts on Oct. 15.

There are a few exceptions: You can sign up for a new plan after Jan. 31 if you get married, have a baby, or lose your health coverage. But the Obama administration is cracking down on use of other special open enrollment periods after insurer complaints that people were waiting to buy coverage until they were sick. (As long as you buy a plan with minimum essential coverage during open enrollment, insurers can not reject you based on a pre-existing condition, and the plans can't impose annual or lifetime caps on essential benefits.)

If you already have an Obamacare plan that you bought on Healthcare.gov, you can switch plans anytime before Sunday. You can save a lot if you shop: So far, people who have switched to a cheaper plan have saved $516 a year, on average, according to HHS.

Remain uninsured, and you'll pay up at tax time in 2017. The average tax penalty for not having insurance this year is estimated to be $969, according to the Kaiser Family Foundation. (Calculating the tax is complicated: It's the higher of either 2.5% of your income, capped at the average price of a bronze plan—$2,484 this year—or $695 per adult and $347.50 per child in your family, capped at $2,085 total.) You can get an exemption from the tax if you earn too little to file a tax return, if you're uninsured for less than three months, or if you have another qualified hardship.

Some people choose not to purchase health insurance because Obamacare premiums can be high, especially without the subsidy. However, if you remain uninsured, you won't be protected against exorbitant medical bills for an unexpected medical emergency. Could you pay $400,000 in medical costs if you were hit by a train? Most people can't—which is why you need insurance.