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Open up wide, and say "Obamacare."
President Barack Obama's landmark health-care reform law hit a massive milestone Tuesday, as new government-run marketplaces finally opened for business and began enrolling what is expected to be 7 million Americans in newly affordable, comprehensive health insurance plans by 2014.
The six-month roll-out comes amid continued partisan battles over funding for the law that sparked Tuesday's government shutdown, remaining widespread public ignorance about the law's details and reports from around the country that technical problems were plaguing some those health marketplaces, known as exchanges.
At least 24 out of the 36 state marketplaces being run by the federal government posted error messages after opening at 8 a.m. because of a rush of people trying to log in to them online. More than 1 million people in the last day visited the web site www.healthcare.gov operated by the U.S. Health and Human Services Department to promote the exchanges.
"We apologize that wait times on the site and hotline are longer than expected!" tweeted HealthCare.gov, the Twitter feed for the site.
The website for New York State's health exchange, which is being run by the state, received a stunning 2 million hits in the first two hours of operation, leading to delays, according to officials.
"We are working our technical teams and experts are standing by—they are working to make certain that the website responds more quickly," said New York State of Health exchange chief Donna Frescatore. "Our call center wait time here is just about five minutes, so that's longer than we would otherwise experience, but they are getting to callers and answering their questions."
Other delays around the country included Maryland and Minnesota, which postponed their openings until Tuesday afternoon.
(Read more: 8 things to know about Obamacare)
Experts had predicted the first day would not go flawlessly. And the Obama Administration on Tuesday reiterated the benefits they expect from the rollout, which is aimed at the 30 million Americans who don't have healthcare through their employer, Medicare, or Medicaid.
A rush to the exchanges
"For years, the financial, physical or mental health of millions of Americans suffered because they couldn't afford the care they or their family needed," said HHS Secretary Kathleen Sebelius. "But thanks to the health care law, all of that is changing. Today's launch begins a new day when health care coverage will be more accessible and affordable than ever before."
Obama himself Tuesday touted the ACA as he blasted Republicans in the House of Representatives for forcing a limited shutdown of the U.S. government after he and Senate Democrats staunchly refused to delay his signature health-care law.
(Read more: You think the Obamacare fight is ugly?)
"There's going to be some glitches along the way in the sign-up process that we will fix," Obama said in an address outside the White House, where he was flanked by people whom he said would benefit from the law. But, he noted, "There were five times more users in the marketplace this morning than had ever been in" the government website for Medicare users at any one time.
"This gives you a sense of how important this is to millions of Americans around the country, and that's a good thing," Obama said.
Obama compared the technical problems Tuesday with the recent rollout of Apple's new operating system.
"Within days they found a glitch and they fixed it," Obama said. "I don't remember anyone suggesting that Apple stop selling iPhones or iPads or shut down the company if they didn't."
"I will not give in to reckless demands by some in the Republican Party to deny health-care coverage to millions of Americans," he said.
'A huge day'
Larry Vernaglia, leader of the Boston law firm Foley & Lardner's health-care industry team, said the launch compares with the establishment of the government's Medicare program in the 1960s. "It's a huge day," Vernaglia said.
(Read more: The selling of Obamacare)
"I don't necessarily think that all of a sudden some kind of health-care nirvana is going to appear in America," Vernaglia said. "But I think people are going to see a benefit."
Vernaglia said he expected that the first wave of people to sign up will be people with pre-existing health conditions. He and other experts expect a significant surge of enrollment around Dec. 15, the last day that people can enroll and ensure that their coverage begins Jan. 1, and not later in the year.
How Twitter is following Obamacare's Big Day
The new health insurance marketplaces, also called exchanges, are opening in all 50 states and the District of Columbia, and will offer competing plans from private insurers for sale, all with standardized benefits. People who currently lack insurance, or who lack affordable coverage from their employer, can go online to compare the prices from the plans being offered, and then enroll. Under the law, nearly all Americans must have health insurance by the beginning of 2014 or face a tax penalty.
(Read more: Obamacare 'not a bad thing': Hospital chief)
"I need to get it," said Garvin Meyers, a 35-year-old car-service driver who lives in San Francisco.
Until he spoke to a CNBC.com reporter last week, Meyers was unaware that California's exchange Covered California was opening Tuesday, and that a website for the exchange was already live, with prices for the insurance available to view.
"I knew it was coming, but I didn't realize it was set up," Meyers said.
Eligibility status errors
Meyers, who is single, earns about $40,000 per year. That income level makes him—along with many others expected to enroll on the exchanges—eligible for government subsidies to reduce the cost of the insurance.
But as of late last week, the federal government's data hub reportedly had a 33 percent error rate for determining eligibility for those subsidies, and software engineers were working round-the-clock to fix the issue.
Insurers are counting on relatively young, healthy people like him to enroll to offset the benefits they will have to pay out to people who have pre-existing conditions, or who get sick. Under new Obamacare rules, insurers cannot deny coverage for pre-existing conditions, charge higher rates for the sick or bounce people from coverage if they fall ill.
(Read more: How do Obamacare exchanges work?)
"We're ready to go," said Kevin Counihan, the head of Connecticut's health exchange, during an interview Monday on CNBC's "Closing Bell."
"We're actually looking forward to getting going," said Counihan, whose Access Health CT exchange is operating retail outlets where people can walk in off the street, receive information about their insurance options and then sign up for coverage.
Recent surveys have shown that a majority of people don't understand enough about health insurance terms, such as deductibles, copays and coinsurance, to understand how much coverage really costs.
Many still unaware of launch
Other surveys have shown that most people are unaware of the exchanges, and that the majority of people most likely to benefit from them—those uninsured with low incomes—are particularly ignorant about the marketplaces.
Vernaglia, the Foley & Lardner health-care lawyer, dismissed concerns that the law is too complicated to people, and hence will hamper enrollment. "People don't understand their taxes, but seem to get those bloody things filed every year," he said.
Vernaglia also scoffed at the idea that the technical glitches some exchanges have reported will doom Obamacare by discouraging enough people from enrolling to keep premium prices affordable.
(Read more: Call centers standing by for Obamacare "boost")
"In any system, there will be glitches," he said. "American consumers are kind of used to things not working on the first day. ... There are problems with Apple's mapping technology—does that mean that people aren't going to use the iPhone?"
Still, Vernaglia said, "There's going to have to be a lot of public education" about the exchanges.
Ron Pollack, who started the advocacy group Enroll America to encourage people to sign up on the Obamacare exchanges, said the six-month-long enrollment period, coupled with a nearly two-month-long enrollment period next fall for coverage in 2015, will provide a lot of time to educate people and get them to enroll.
To date, Pollack said, "Virtually the entire discussion has been about the politics of the Affordable Care Act."
"But now that we're about to begin the enrollment process, people are starting to focus, and asking, 'What does it mean to me, what does it mean to my family?'" he said.
—By CNBC's Dan Mangan. Follow him on Twitter @_DanMangan.