The launch marks a milestone for Obama's signature domestic policy achievement, which aims to provide subsidised healthcare to millions of the uninsured, the most ambitious US social program since Medicare was introduced in the 1960s.
Obama is scheduled to meet and pose for pictures in the Oval Office with a group of Americans who stand to benefit from the programme, while Vice President Joe Biden and first lady Michelle Obama will also promote the law via media channels.
The first day of online enrollment in the health insurance plans was going ahead despite a partial shutdown of the US government after the failure of the US Congress to pass spending bills to fund government operations in the fiscal year that begins on Tuesday.
The marketplaces, or exchanges, require health plans to provide a broad range of essential benefits that were not necessarily part of individual policies in the past, including mental health services, birth control and preventive care. The coverage is linked to other insurance market reforms and new consumer safeguards, including a ban on discrimination based on gender and health history.
The healthcare law also mandates that Americans obtain insurance or pay a fine.
"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," US Department of Health and Human Services Secretary Kathleen Sebelius said in a statement on Tuesday. "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."
Republicans have fought for months to delay or stop Obamacare, most recently triggering a shutdown of the federal government on Monday night by insisting that a routine funding measure include a delay in Obamacare, which the Democratic-controlled Senate rejected.
"The Affordable Care Act is moving forward. That funding is already in place. You can't shut it down," Obama told his Republican opponents in a televised statement at the White House on Monday.
Officials running the new exchanges braced for computer problems that could hamper the enrollment effort. The federal government opened websites for 36 states through its www.healthcare.gov site at 8 am EDT (1200 GMT).
But early checks on 18 of these state sites for some users called up error messages such as: "We have a lot of visitors on our site right now and we're working to make your experience here better. Please wait here until we send you to the login page." Others who were able to begin to set up an account were halted at a page for security questions.
As many as 7 million Americans are expected to sign up for insurance in 2014 through the exchanges, which will accept applications through March 31. An additional 8 million people are expected to receive health benefits through an expansion of the government's Medicaid program for the poor.
Republicans have blamed Obamacare's requirements for pushing up the cost of health insurance for business and individuals, a charge the Democrats deny.
"What I want is to keep the government running and at the same time to deal with the harms, the millions of Americans who are ... at risk of losing their healthcare, are facing skyrocketing insurance premiums," Texas Senator Ted Cruz, who has been leading the charge among Republicans in Congress to
defund the law, said in an interview with CNN.
The Patient Protection and Affordable Care Act has been the object of intensive Republican attack since it was signed into law in 2010. Its foes tried and failed to use the U.S. Supreme Court and a presidential election to get it overturned in 2012.
In the early planning, the administration aimed to create new healthcare markets that would make shopping for insurance as simple as buying an airline ticket online. But repeated delays and technical difficulties mean the new sites in many states will not have all of their functions ready in the first weeks, or perhaps longer.
Minnesota officials said on Monday that they were not yet sure what time their state's exchange would launch, and that the timing would only be determined after further testing on Tuesday morning to see if the system connected properly with federal government's network for determining subsidies.
The US Department of Health and Human Services, which will operate federal marketplaces in 36 states that are not running their own, has also said that technical glitches are likely.
"We will fix them and move on. Is it a sign that the law is flawed and failed? I don't think so. I think it's a sign that we're building a piece of complicated technology," Sebelius said.
Senior administration officials and organizers working to help reach the uninsured with news of the law's benefits believe enrollment will get off to a quiet start on Tuesday and build slowly through the next six months.
The first enrollees are likely to be people with pre-existing health conditions and older people who have had a hard time obtaining coverage. But the law's success will depend on young healthy adults, whose lower risk profile is needed to compensate for higher cost beneficiaries.
The law remains unpopular, however, with 46 percent of the public. Anti-Obamacare forces have spent hundreds of millions of dollars in television advertising, outspending Obamacare supporters by more than four-to-one. Meanwhile, millions of potential beneficiaries do not know the law exists.
Officials said Tuesday would also see a ramp-up in the administration's multimillion-dollar media campaign to reach prospective beneficiaries through television, Twitter, Facebook and social organizations including churches. In particular, they are targeting young and healthy Americans. The advertising campaign is targeting black and Hispanic men between the ages of 18 and 35 in large cities in Florida, Texas, Illinois and California.