CHICAGO (AP) — The deadline has passed, and so too the surprise grace period, for signing up for health insurance as part of the nation's health care law.

Now what?

For those who were able to navigate the glitch-prone and often overwhelmed HealthCare.gov website, there's still work to be done to make sure success online leads to actual coverage come the new year.

The first step experts recommend is to call your insurance company and double-check they received your payment.

What if you missed the Christmas Eve deadline and still want insurance in 2014, as the health law requires of most Americans? You may be without health insurance for a month, but you can still sign up for coverage that will start in February.

"Be patient, because they're trying to help you," said Tina Stewart, a 25-year-old graduate student in Salt Lake City who succeeded in enrolling in a health plan Tuesday morning. "It will take time."

The historic changes made by the Affordable Care Act take full effect on Jan. 1. People with chronic health conditions can no longer be denied health insurance. Those who get sick and start piling up medical bills will no longer lose their coverage. Out-of-pocket limits arrive that are designed to protect patients from going bankrupt.

But unless the 1 million Americans who have so far enrolled for coverage via the new marketplaces make sure their applications have arrived at their new insurance companies without errors, some may find they're still uninsured when they try to refill a prescription or make a doctor's appointment.

"The enrollment files have been getting better and more accurate, but there is still work that needs to be done," said Robert Zirkelbach, a spokesman for America's Health Insurance Plans, a trade group that represents the private insurance industry. "The health plans are still having to go back and fix some of data errors coming through in these files."

If everything went smoothly, consumers can expect to see a welcome packet arrive in the mail from their insurance company, Zirkelbach said. If not, a phone call to the insurer might clear things up.

"If a consumer signed up yesterday, they shouldn't expect the health plan to have their enrollment application today," Zirkelbach said. "Allow a couple of days to receive and process those enrollments."

Paying the first premium is crucial. Because of the changing deadlines for enrollment, most insurers have agreed to allow payments through Jan. 10 and will make coverage retroactive to Jan. 1, he said.

Anyone who missed the Christmas Eve deadline to enroll for insurance to start in January can still apply at HealthCare.gov for coverage to begin later. The federal website serves 36 states, but also directs people elsewhere to the online insurance site serving their state. The site also offers directions to local agencies offering in-person help.

After the disastrous rollout in October, the federal website received 2 million visits on Monday, and heavy — but not as heavy — traffic on Tuesday. White House spokeswoman Tara McGuinness said she had no immediate estimate of visitors Tuesday or how many succeeded in obtaining insurance before the midnight Christmas Eve deadline. The unexpected one-day grace period was just the latest in a string of delays and reversals.

Unless you qualify for Medicaid, you'll pay a monthly "premium" fee to an insurance company for coverage. Before the company covers actual medical costs, you may have to pay a certain amount called a deductible, in addition to a possible set fee for a doctor visit (copay) or a percentage of the cost of a medical service (coinsurance).

Federal tax credits are aimed at helping make premiums more affordable for households earning between 100 percent and 400 percent of the federal poverty line. That's $11,490 to $45,960 for an individual, $23,550 to $94,200 for a family of four.

Finally, note the next significant deadline isn't for a few more months. If you don't have coverage by March 31, you'll pay a tax penalty next year of $95 or 1 percent of your income, whichever is higher.

Ron Pollack, president of Families USA, a liberal advocacy group that has led efforts to get uninsured people signed up for coverage next year, said that's the deadline that matters most.

"The real significant deadline is March 31," Pollack said. "The enrollment period extends for another three months."