The "Obamacare" insurance exchanges struggled to handle a flood of consumer interest that closed the website for much of the day, and caused start-up delays for most of the marketplaces run by states.
New York officials said the state's exchange had more than 2 million visits in the first few hours of operation. California reported seeing as many as 10,000 hits a second on its site.
While Republicans pounced on the breakdowns as evidence the law doesn't work, President Barack Obama said the volume "gives you a sense of how important this is to millions of Americans."
The problems created a rocky debut for the system at the center of the Affordable Care Act's efforts to cover more of the 48 million uninsured Americans.
The exchanges are supposed to help consumers access federal subsidies and choose from a menu of private insurance plans that take effect Jan. 1, when the law requires all Americans to obtain insurance.
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"Like every new law, every new product rollout, there are going to be some glitches in the sign-up process along the way that we will fix," Obama said Tuesday.
While the federal site was down for much of the day, administrators "added capacity and made adjustments" to put it back into service by late afternoon, said Marilyn Tavenner, administrator of the Centers for Medicare & Medicaid Services, which manages the site. Tavenner declined to say how many people had enrolled through the exchanges.
Despite the first-day crush, enrollees don't have to complete the process until Dec. 15 to guarantee coverage on Jan. 1.
The president is "the same guy who promised his health care ideas would make Americans' premiums lower, and that they'd be able to keep the plans they liked," Kentucky Sen. Mitch McConnell, leader of the chamber's Republicans, said in an email. "So forgive me for being a little skeptical, given how these other rosy scenarios have played out."
While delays persisted, frozen and sluggish websites did improve through the day Tuesday. Of the 14 states and Washington, D.C., that have built their own exchanges, all but five had allowed users to register by midafternoon.
Prices for the lowest tier of plans average $249 a month. People with incomes less than about four times the poverty level will get discounts on their premiums by way of tax credits. A family of four qualifies with an income of less than about $94,000.
The Obama administration had warned of early problems for weeks.
The $1.4 trillion Affordable Care Act requires most Americans to obtain health insurance starting next year or pay a fine. The vast majority of people, already covered by a workplace plan, Medicare or Medicaid won't be affected.
The administration is seeking to get about 7 million people to buy policies through the exchanges in the open enrollment period that runs through March. The federal site had 2.8 million visitors since midnight and 81,000 more people used an exchange call-in line, Tavenner said.
Teajai Kimsey, 49, of Wichita, Kan., runs the website Internet Idea Girl and is uninsured. When she logged on to healthcare.gov Tuesday morning, it took her about five minutes to get into the system, she said. Then there was a glitch.
"If you don't know the Web well, it will be really discouraging," Kimsey said in a telephone interview.