The new extension follows a 24-hour "grace period" that was granted on Monday -- beyond the original deadline of Monday 11:59 pm --for benefits that would kick in on Jan. 1.
In an blog Tuesday on the HealthCare.gov website, the Obama Administration said that people who could prove that trouble on the Healthcare.gov website had hindered them from signing up would be granted an extension.
"Even though we have passed the Dec. 23 enrollment deadline for coverage starting Jan. 1, we don't want you to miss out if you've been trying to enroll," the administration said in the blog.
"Sometimes despite your best efforts, you might have run into delays caused by heavy traffic to HealthCare.gov, maintenance periods, or other issues with our systems that prevented you from finishing the process on time. If this happened to you, don't worry, we still may be able to help you get covered as soon as Jan. 1," the message added.
The blog advised visitors: "Contact the Marketplace call center at 1-800-318-2596 (available 24/7; closed December 25). TTY: 1-855-889-4325. Tell our customer service representative that you've been trying to enroll and explain why you couldn't finish by the deadline. They can tell you what you can do to finish your enrollment and still get covered for 2014."
There was a record amount of traffic on Healthcare.gov on Monday, The New York Times reported, and health officials wanted to make sure that people who are looking for coverage can get it.
In most states, Monday, Dec. 23 had been the deadline for selecting a plan that would take effect on the first day of the new year.
"We would really encourage people to start now. Don't wait until the deadline to enroll," Cheryl Fish-Parcham, deputy director of health policy at Families USA in Washington, D.C., said last week.
People need to leave themselves enough time to gather the information they need to complete an insurance application, select a health plan and pay the premium by the health plan's deadline, she said.
The pre-Christmas race to buy health insurance is another consequence of the troubled launch of the Affordable Care Act's HealthCare.gov website and website difficulties in a number of state-run health insurance exchanges. Since the October launch of the health exchanges, sign-up and premium-payment deadlines have been extended to give people more time to enroll for coverage, but the new cut-offs come amid the holiday rush.
Many people aren't aware of the various deadlines under the law, sometimes called Obamacare. What's more, the deadlines may vary by state and by health insurer, health insurance agents and brokers said.
"There is a lot of confusion," said Anna Causey, vice president of Combined Insurance Services Inc., a Pensacola, Fla.-based benefits broker.
Some people mistakenly believe they have until Dec. 31 to enroll in a plan that takes effect on Jan. 1, Causey said. Others don't realize they could pay a federal tax penalty if they don't have health insurance in place by March 31, she said.
Under the Affordable Care Act, most adults will pay a $95 penalty -- or 1 percent of income -- in 2014 if they don't have health insurance coverage. The penalty rises to $695 -- or 2 percent of income -- by 2016.
To avoid the penalty, people must enroll in a plan by Feb. 15 or qualify for an exemption from the penalty, Causey said.
If you're in the market for health insurance, here are some key dates to keep in mind:
What's the latest I can enroll in coverage for Jan. 1?
Consumers shopping on HealthCare.gov, the federal portal serving individuals in 36 states, originally had until 11:59 p.m. ET on Monday, Dec. 23, to enroll if they want coverage to take effect on the first day of the new year. That was extended by 24 hours and now is extended further for those people who had problems signing up at HealthCare.gov.
What if I enroll through my state health insurance exchange?
Deadlines for Jan. 1 coverage may differ in states that operate their own health exchanges.
Health insurers in Maryland, for instance, have agreed to extend the sign-up deadline through Dec. 27, state officials announced Tuesday. Consumers must pay their premiums by Jan. 15, the officials said.
Make sure to check with your state health exchange.
Can I enroll after Jan. 1?
Open enrollment for 2014 runs through March 31. If you buy coverage, say, on Feb. 10, it won't kick in until March 1. If you wait until March 31, your policy will take effect May 1.
There is no deadline for signing up for Medicaid or the Children's Health Insurance Program.
If I enrolled in a private health-exchange plan by Dec. 23, when is my premium due?
Recently, the federal government directed insurers to accept payment by Dec. 31 and encouraged health plans to push the deadline further.
Consumers who signed up by Dec. 23 and pay the first month's premium by Jan. 10 will have coverage on Jan. 1, the industry group America's Health Insurance Plans announced last week.
However, the federal government cautions that not all health insurers are extending the payment deadline, and some may require payment on or before Dec. 31, 2013.
"Once you've enrolled, check with your plan that they've received your enrollment and what is the premium payment deadline and how do you go about paying your first month's premium," Fish-Parcham advised.
Is it better to enroll now or sometime before March 31?
Insurance brokers say it depends on your situation.
"The (health plan) options will not change," said Karen Sweeney, benefit consultant with PIT4 Medical Insurance Consultants, in Mesa, Ariz.
She recommends that individuals who are uninsured or who are losing coverage on Jan. 1 "get with an educated insurance broker and make a selection by Dec. 23."
People who have coverage that carries over into 2014, however, don't necessarily need to rush to meet the cutoff time, brokers said.
Need help with your insurance application? HealthCare.gov has tips for getting health insurance coverage.
To read a related HealthDay story on last-minute exemptions for people who've lost their health insurance under the Affordable Care Act, click here.