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And you thought Obamacare wasn't popular.
Launched Tuesday, the long-awaited online state insurance exchanges were promptly swarmed by millions of people looking to check out prices and sign up for coverage.
But the surge temporarily stalled or froze many exchanges, including the Healthcare.gov portal run by the federal government, which is operating exchanges for 36 states.
Between midnight and late Tuesday afternoon the website had nearly 3 million visitors, many of whom were greeted by a message saying, "Please wait," rather than being connected to pricing information or an enrollment page.
Two million New Yorkers visited the website of their state-run exchange in its first two hours, overwhelming the system. Several state-run exchanges, including Maryland's, delayed opening for several hours, while Hawaii postponed opening for the day.
Still, some people were able to enroll, as many more will before the enrollment period ends on March 31.
Observers said that what federal officials called the "extraordinary volume" suggested that the government-run exchanges may well be on track to achieving the Affordable Care Act's goal of providing affordable, comprehensive health coverage to 7 million or more people in 2014. The volume came even though recent surveys showed low overall public awareness of the exchanges' existence and operation.
(Read more: Obamacare explained)
"They are doing gangbusters," said Chini Krishnan, CEO of the online insurance market GetInsured.com. "They should be very, very happy today. It is awesome news."
The exchanges are offering insurance plans at competing prices to the tens of millions of Americans who lack coverage. Many will be eligible for government subsidies to offset the cost. Nearly all Americans must obtain health insurance—either through the exchanges, their employers, Medicare or Medicaid—by 2014 or face a tax penalty.
During a call with reporters Tuesday afternoon, Marilyn Tavenner, administrator of Centers for Medicare and Medicaid Services, repeatedly declined to disclose the total number of enrollees or when it would be disclosed.
(Read more: Obamacare exchanges: CNBC explains)
"We're not releasing that information yet," Tavenner said.
But CMS Policy Director Chiquita Brooks-Lasure said, "We are certainly very pleased with the remarkable interest we have received."
President Barack Obama also cited the visitor volume in an address in the White House's Rose Garden, where he was joined by people who he said would benefit from the plans being offered on the exchanges.
He also blasted Republicans in the House of Representatives for forcing a federal government shutdown over demands that he and Senate Democrats postpone by one year the mandate that individuals obtain insurance.
"Now, like every law, every new product rollout, there are going to be glitches in the sign-up process along the way that we will fix," Obama said. "Consider that just a couple of weeks ago, Apple rolled out a new mobile operating system. And within days, they found a glitch so they fixed it. I don't remember anyone suggesting Apple should stop selling iPhones or iPads—or threatening to shut down the company if they didn't.
"As long as I am president, I will not give in to reckless demands by some in the Republican Party to deny affordable health insurance to millions of hard-working Americans," Obama said.
Blue Cross/Blue Shield of Florida is selling insurance in all 67 counties in the state through the federal exchange.
"We're definitely seeing a lot of volume, which indicates a fair amount of interest going on," said Florida Blue CEO Patrick Geraghty. In addition, he said, phone traffic was "up about 20 percent" during the rollout.
While it was hard to know for sure how many visitors to the exchange website would become customers, Florida Blue expects the number of customers to grow from the current 300,000 to between 375,000 and 400,000 during the enrollment period, he said.
(Read more: Obamacare deadlines)
Andrew Rubin, vice president for medical center clinical affairs and affiliates at NYU Langone Medical Center in New York, said he was "disappointed" by the site glitches and slowdowns that he and others experienced Tuesday.
"I feel like someone should have figured that out," said Rubin, who hosts the call-in show "Health Care Connect" on Sirius XM satellite radio.
But, he added, "the good news is there is six months to get people on there."
"I'm going to tell people not to worry, not to panic—you don't have to sign up for insurance today," said Rubin, whose radio show has been dominated by questions about Obamacare in recent months. "I'm going to tell people to wait. You don't have to do it today and get frustrated by the process."
EHealthInsurance.com had, like GetInsured.com and several other online sellers, had expected to begin enrolling people in subsidy-eligible plans when the federal exchange opened Tuesday.
But eHealth CEO Gary Lauer and GetInsured's Krishnan told CNBC.com that their companies received required data from the government only a few days ago and won't be able to offer those plans for several weeks.
"I think they've got their hands full, and it just took time to get here," Lauer said, referring to the CMS. "This is a very complex task."
Though he said he wasn't happy with the delay in getting eHealthInsurance.com connected with the federal exchanges (which will give his company business) he expects the "real volume" of enrollment to come much closer to Dec. 15. That's the deadline by which people must sign up and make initial premium payments for coverage to kick in by Jan. 1.
Krishnan echoed that, saying, "The word in our shop is that we think consumers want to click on the 'Learn more' button today, not the "Buy now' button today."
(Read more: Obamacare cost-cutting)
—By CNBC's Dan Mangan. Follow him on Twitter @_DanMangan