(Credit: Joe Raedle/Getty Images) Angel Rivera and wife Wilma Rivera sit with Amada Cantera, an insurance agent, as they try to purchase health insurance under the Affordable Care Act at the Mall of Americas in Miami, Dec. 22, 2013.

For Ted and Maxine Baumgartner of Ft. Wayne, Ind., their first day as owners of a 2014 Obamacare insurance policy can be summed up in one word: relief.

The couple's months-long odyssey to buy coverage for Maxine through HealthCare.gov was a torturous experience that encapsulates everything that went wrong with the rollout. It also shows how persistence can ultimately pay off.

Baumgartner, 62, is among an estimated 2 million Americans who've selected health plans through the Obamacare insurance exchanges since October and will start 2014 with protection from a potential medical and financial nightmare.

"Even though she only needs private insurance for another two and a half years, she has to have it, or else?" said Ted Baumgartner, a 67-year-old Medicare beneficiary who helped his wife purchase an individual plan.

"She has to be covered even if only for something that could - hopefully not - but could happen," he said of his wife, who's not yet eligible for Medicare.

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Obtaining that coverage was an aggravating process. Maxine, a part-time worker at Jo-Ann Fabric and Craft Stores, first saw her existing insurance plan cancelled earlier this year because it didn't comply with the Affordable Care Act. Then, when she turned to the government website to shop for an alternative, she faced technical glitches at every turn.

After nearly 80 hours online and more than a dozen hours on the phone, an enrollment application that never made it to the insurer, and a stinging case of premium sticker-shock, Baumgartner says the first payment to Anthem of Indiana is finally in the mail.

"If you really have to have the insurance, and it appears that the government is telling you that you're going to, then just hang in there because it can't get any worse," Ted Baumgartner said.

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The Baumgartners are among the millions of Americans who are for the first time receiving government help to pay the bill. Their $699 monthly premium for a mid-tier "silver plan" was offset by a $595 a month tax subsidy, leaving a balance of just $104 out of pocket.

That amount is still about four times what they paid last year for coverage, Baumgartner said, but the new plan is loaded with added benefits. Of those, however, Ted Baumgartner has a mixed view.

"Some of the free preventive care would probably help some. But a 62-year-old woman doesn't need maternity. She doesn't need abortion," he said.

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There is also concern that visits to Maxine Baumgartner's regular physician might not be covered under the new policy. Details of the provider network have yet to arrive in the mail.

Baumgartner is also still waiting for an insurance card, that critical piece of information needed to access care in the New Year.

The Department of Health and Human Services Tuesday urged consumers to contact their insurance company as soon as possible to verify coverage and obtain a card. Technical problems with the enrollment system have created numerous cases of insurers having no record of some Americans who think they're signed up.

Obama administration officials are hoping to avoid embarrassing reports of people showing up to try their new coverage only to find that it hasn't taken effect.

"Before you go to the doctor or pharmacy using your new insurance for the first time … make sure to get your insurance card or a temporary card with your new plan's information," HHS wrote in a blog post. "If you don't have your card yet, ask your insurance company to give you another way to confirm your coverage."

And, the agency says, don't forget to pay. Submitting the first month's premium is the only way to guarantee coverage in January. In most states for most plans, consumers have until Jan. 10 to cut the check, with coverage retroactive to Jan. 1, according to the insurance industry trade group, America's Health Insurance Plans.