The deadline for enrolling in policies that start on January 1 had already been repeatedly delayed and was last fixed at midnight on yesterday, after problems with the web site hindered the process.
But now, Health and Human Services, which administers the program, said if anyone failed to finish their enrollment by that time, they could still get a policy for the new year.
"Sometimes despite your best efforts, you might have run into delays caused by heavy traffic to HealthCare.Gov, maintenance periods, or other issues," read a message on the site.
It provided customer service numbers and told consumers to "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."
The Affordable Care Act, President Barack Obama's top domestic achievement to date, is designed to offer insurance to millions of Americans who have never been able to secure it before -- some because of pre-existing health conditions like heart disease that insurers were unwilling to cover.
Obama told reporters on Friday at a year-end press conference that more than a million American had chosen new insurance plans using the new health care system.
But the litany of problems with the government website, healthcare.Gov, has played into the hands of Republicans, who say the federal government has no business intervening in the private health care market and should not be dictating health choices to Americans.
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