Error rates were lower than 1 in 200, and pages loaded quickly, in less than a half-second, officials said.
For a multitude of reasons, including technical difficulties with the site or trouble understanding the instructions, thousands of people sought telephone help and wound up waiting on hold on Christmas Eve at the government's call center.
Ian Stewart of Salt Lake City said he and his wife, both students, had been trying for weeks to complete their application on the federal site, thwarted by computer error messages each time.
On Tuesday morning, while visiting relatives in Colorado for Christmas, they reached a call center counselor who succeeded in enrolling them. The "silver" plan they chose will cost them $241 a month after a cost-lowering tax credit.
"We're relieved that we got it working, elated that we got insurance again and very frustrated that it took this long," Stewart said.
More than 110,000 people had called the government's help line by Tuesday afternoon, with wait times averaging 27 minutes, officials said. On Monday, the call center received more than 250,000 calls, a one-day record.
Monday was the sign-up deadline for people wanting coverage at the start of the new year. But the Obama administration pushed back the deadline a day to deal with heavy traffic from procrastinators.
"We see this intense traffic as a sign that people are eager for affordable health insurance," said Julie Bataille, a spokeswoman for the CMS, the federal agency in charge of the overhaul.
While there were no immediate reports of any major glitches, the White House said that people who can show they missed the deadline because of problems with the website may still be able to get covered by Jan. 1 on a case-by-case basis. Those who try to sign up for the first time after the deadline passes can still get coverage, but it won't start until Feb. 1.
The one-day grace period was just the latest in a string of delays and reversals, and critics of President Barack Obama's signature program seized on it as more evidence that the overhaul is in trouble.
"The amazing, ever-expanding deadline? It's clearly a sign of desperation by the administration to do everything they can to increase the number of people signing up," said health economist Gail Wilensky, who ran Medicare for President George H.W. Bush.
The website went through extensive hardware and software upgrades to make it more reliable and increase its capacity.
When the number of simultaneous users reached 60,000 on Monday, site operators employed a queuing system that allows people to either wait or give an email address to be invited back later, the government said. More than 129,000 users gave their email.
On Tuesday, traffic wasn't heavy enough to trigger the system, McGuinness said in the afternoon.
Many states operate their own online marketplaces for buying coverage, and some of them also extended their deadlines.
The insurance industry, too, has pushed back deadlines for payment, with most health plans allowing customers to pay by Jan. 10 and still get coverage retroactive to Jan. 1.
"With deadlines that keep changing, insurers want to alleviate confusion," said Robert Zirkelbach, spokesman for America's Health Insurance Plans. "Health plans are going to do everything they can to help consumers with the enrollment process."
Obama said late last week 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.