Republican opposition to the plan forced the US government to close its doors and kept hundreds of thousands of workers home without pay, but administration officials vowed health reform would forge ahead.
Known widely as "Obamacare," the Affordable Care Act was passed by Congress and signed by Obama in 2010, with a promise to help 30 million uninsured people get health care coverage.
Despite its ambitions to revolutionize American health care, the plan is not free and will not be able to cover tens of millions of people in America who lack full insurance.
Advocates have touted it as a major step forward, while opponents like Republican House speaker John Boehner have insisted the law "is not ready for prime-time."
Indeed, in the first part of the day Tuesday, the new health insurance exchanges that were to begin enrolling people via the website healthcare.gov were jammed.
Frustrated users flocked to Twitter to complain that healthcare.gov and others linked to the exchanges were not working.
An attempt by an AFP reporter to check the prices offered in Virginia resulted in the message: "Important: Your account couldnt [sic] be created at this time. The system is unavailable."
The NY State of Health site said that "overwhelming interest" had led to two million visits in the first two hours of the launch, and asked people to come back later if they had been unable to log in.
"Today is launch day for Obamacare and so far it's like a giant online traffic jam on the first day of summer vacation," said analyst Jeff Kagan.
"No one knew what to expect, but chaos is what we have."
Obama vowed that the website would speed up later in the day, and said it had been slowed because more than one million people visited before 7:00 am (1100 GMT) alone.
"There were five times more users in the marketplace this morning than have ever been on Medicare.gov at one time. That gives you a sense of how important this is," said Obama.
"We are going to be speeding things up in the next few hours to handle this demand that exceeds anything we expected."
Obama said most people should be able to get coverage for less than $100 per month.
About seven million Americans are expected to seek coverage by 2014, according to the Congressional Budget Office.
The policies available on the health exchanges range in price according to a person's income, location, family size and the level of coverage desired on a scale of bronze, silver, gold or platinum.
All Americans must sign up for some kind of health insurance by January 1 or face a fine.
The government said last week there will be around 53 plans to choose from in the federally-facilitated marketplace.
Most Americans have health insurance -- 82.6 percent according a July report from the Department of Commerce based on data from the 2010 Census.
About half get it through their employer, and about 30 percent are enrolled in government programs like Medicare, mainly for seniors, and Medicaid, which covers the poor and disabled.
That leaves 17.4 percent of Americans uninsured, or about 53 million people.
An analysis in the journal Health Affairs earlier this year projected that around 30 million Americans will still not get health insurance through the Affordable Care Act.
Those gaps are due in part to the Supreme Court's decision to allow some states to opt out of expanding Medicaid programs, coupled with a cut in funding to safety-net hospitals.
The Affordable Care Act "will leave tens of millions uncovered. It will do little to alter racial disparities in coverage," said the Health Affairs report published in June.
"The ACA, whatever its merits, will fall well short of its stated goal of providing affordable care for all Americans."