It was the latest in a series of pushed-back deadlines and delays that have marked the rollout of the health care law.
But federal officials urged buyers not to procrastinate.
"You should not wait until tomorrow. If you are aiming to get coverage Jan. 1, you should try to sign up (Monday)," said Julie Bataille, a spokeswoman for the federal agency in charge of the overhaul.
Bataille said the grace period -- which runs through today -- was being offered to accommodate people from different time zones and to allow for any technical problems that might result from a last-minute rush of applicants.
The HealthCare.gov site had a disastrous, glitch-prone debut in October but has gone through extensive improvements to make it more reliable and increase its capacity, and the administration said the system was running well Monday.
By the afternoon, the site had received a record 850,000 visits, five times the number logged by the same time last Monday, the administration said. Bataille said the system was handling the volume with error rates of less than 1 in 200 and response times of less than one second.
The Obama administration is hoping for a surge of year-end enrollments to show that the technical problems were merely a temporary setback. That would also go a long way toward easing concerns that insurance companies won't be able to sign up enough young, healthy people to keep prices low for everyone.
But the grace period may have been a tacit acknowledgement that the website remains vulnerable to heavy traffic. What's more, the delay offered critics of "Obamacare" another opportunity to argue that the law still isn't working and that President Barack Obama keeps changing the rules.
In Ohio, Lt. Gov. Mary Taylor called the deadline extension "a clear sign Healthcare.gov continues to struggle."
"Consumers are already confused and insurers are overwhelmed with the administration's last-minute changes, yet there seems to be no end in sight," Taylor, a Republican who heads Ohio's insurance department, said.
The administration was careful not to characterize Tuesday as a new deadline or an extension, likening the move instead to the Election Day practice in which people who are in line when the polls close are still allowed to vote.
Monday had been the deadline for Americans in the 36 states served by the federal site to sign up if they wanted coverage at the start of the new year. The remaining states operate their own online marketplaces, and some of them have also extended their deadlines.
As the deadline drew new, more than 1 million people visited the website over the weekend, and a federal call center received more than 200,000 calls.
Roger Colyn, 60, of Des Moines, Iowa, was happy when he left his Monday morning appointment with a state enrollment navigator. She helped him sign up for a "silver" plan that will cost him $10.79 in monthly premiums after government aid is factored in.
"I feel relieved," Colyn said.
Others said they will let the date pass without making a decision.
"I'm in no hurry, though it'd be nice to be able to visit a doctor without stress," said Kyle Eichenberger, an uninsured 34-year-old from Oak Park, Ill., who said he hit a wall on the website when he first tried to enroll early on.
"I'm an Obamacare supporter, though I think it is full of problems," Eichenberger said. "I'd like to see the whole system streamlined to be more user-friendly. Keep the basic idea, but don't make me feel like I'm navigating a maze to get a simple checkup."
The government's original deadline already had been pushed back a week because of the website problems. The extra day will add to the already daunting administrative problems that insurance companies face, such as inaccuracies on applications, said industry consultant Robert Laszewski.
"Insurers would like to have two to three weeks to process applications. Now they're going to have a week, less one more day," he said. "When the day is done, it doesn't help."
The president himself signed up for coverage through the government site over the weekend -- a purely symbolic move since he will continue to get health care through the military as commander in chief. He chose a less-expensive "bronze" plan.
Obama said on Friday that more than 1 million Americans had enrolled for coverage since Oct. 1. The administration's estimates call for 3.3 million to sign up by Dec. 31, and the target is 7 million by the end of March. After that, people who fail to buy coverage can face tax penalties.
Minnesota, one of the states running their own insurance exchanges, extended its Monday deadline to Dec. 31 amid problems with its website and extra-long hold times to reach its help center. Maryland pushed back its cutoff date to Dec. 27. New York extended its deadline to midnight Tuesday.
Nevada stuck to its Monday deadline, and enrollment counselors there reported a surge of interest.
"We have people lined up out our door. We still have walk-ins, people are asking for help. Our phones are ringing nonstop," said Andres Ramirez in Las Vegas.
In Connecticut, which also kept to a Monday deadline, Ronshelle McIntyre, a 41-year-old mother from New Britain, arrived at a state-run insurance store around 9:30 a.m., and by noontime, she was among about 40 people waiting to speak with a specialist. Some were told the wait could be two hours or more.
"I don't mind," said the mother of three. "For health insurance, I think all it's going to cost me is a little bit of time and patience to get it plugged up, you know?"
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