"Hc.gov has surpassed a million site visits so far today," administration officials tweeted after announcing the 24-hour sign-up extension.
"Those who want 1/1 coverage should try to sign up today. With record demand, those who try for 1/1 will have a fail-safe to finish tmrrw."
The White House said Monday even President Obama has gone through the application process, if only symbolically since he gets his health insurance through the military.
"Over the weekend and in advance of today's [since extended] deadline, the president enrolled in a healthcare plan made available by the Affordable Care Act on the DC marketplace," a White House official said. "The act of the president signing up for insurance coverage through the DC exchange is symbolic since the president's healthcare will continue to be provided by the military. But he was pleased to participate in a plan as a show of support for these marketplaces, which are providing quality, affordable healthcare options to more than a million people.
"The president selected a bronze plan."
Obama, who is on vacation with his family in Hawaii, was given "a detailed update" Sunday on the preparations for handling the deadline surge, the official said.
"He was briefed on the efforts to ensure that the website could handle the large amount of traffic that was predicted and on efforts to ensure a smooth transition on Jan. 1," the official said.
Those looking to obtain an individual health plan will have until Jan. 10 to make their first payment, a trade group says. But to be safe, healthcare advocates recommend people make their first payment by Dec. 31.
America's Health Insurance Plans, the industry's largest trade group, says its members will give consumers until Jan. 10 to pay their January premium, provided they choose a plan by the Monday night deadline.
The White House encouraged insurers to relax the Dec. 31 payment deadline and provide coverage retroactive to Jan. 1 for people who paid later in the month.
Some state-based exchanges say they're sticking with the Dec. 31 deadline.
Healthcare advocates recommend if people want to be sure they're covered in January, they should pay the first month's premium by Dec. 31, unless they can confirm they have the 10-day grace period for making the first month's premium.
The administration has stressed, and reiterated Sunday, consumers have until March 31 to buy coverage for 2014 and avoid any penalty.
Ron Pollack, executive director of non-profit healthcare advocacy group Families USA, said it was important for some groups of people to make sure they have coverage in January.
Those groups include people whose pre-existing condition insurance plans end Dec. 31, those who lost coverage when insurers canceled plans that didn't meet minimum Affordable Care Act standards, and people in states where Medicaid is scaling back, he told USA Today.
Medicaid is the state-run health program for low-income families and individuals.
"There's been a special outreach to the people in the high-risk pools and who received termination notices," Pollack told the newspaper. "For those who have not had coverage in the past, but haven't needed coverage, they may not feel quite the same sense of urgency."
Obama had said Friday more than a million people signed up for insurance through the federal and state marketplaces, most of them this month.
"So, all told, millions of Americans, despite the problems with the website, are now poised to be covered by quality, affordable health insurance come New Year's Day," Obama said at a year-end news conference.
The federal agency running HealthCare.gov, the insurance website serving 36 states, said nearly 750,000 people visited the site last weekend through noon Sunday.
Julie Bataille, a spokeswoman for the Centers for Medicare and Medicaid Services, which oversees the website, told USA Today the government expected to be able to handle the volume created by the deadline.
HealthCare.gov can handle at least 800,000 people a day, she said.
In addition, the government added 800 people to telephone call centers, so more than 12,000 people were available to answer questions.