To avoid that fate, Obama needs breakthroughs on three fronts: the cancellations mess, technology troubles and a crisis in confidence among his own supporters.
Working in his favor are pent-up demands for the program's benefits and an unlikely collaborator in the insurance industry.
But even after Obama gets the enrollment website working, count on new controversies. On the horizon is the law's potential impact on job-based insurance. Its mandate that larger employers offer coverage will take effect in 2015.
For now, odds still favor the Affordable Care Act's survival. But after making it through the Supreme Court, a presidential election, numerous congressional repeal votes and a government shutdown, the law has yet to win broad acceptance.
"There's been nothing normal about this law from the start," said Larry Levitt, an insurance expert with the nonpartisan Kaiser Family Foundation. "There's been no period of smooth sailing."
Other government mandates have taken root in American culture after initial resistance. It may be a simplistic comparison, but most people automatically fasten their seat belts nowadays when they get in the car. Few question government-required safety features such as air bags, even if those add to vehicle costs.
Levitt says the ACA may yet have that kind of influence on how health insurance is viewed. "An expectation that everybody should have health insurance is now a topic of conversation in families," he says.
That conversation was interrupted by news that the HealthCare.gov website didn't work and that people with coverage were getting cancellation notices despite Obama's promise that you can keep your insurance.
Obama maneuvered this past week to extricate Democrats from the cancellations fallout.
The president offered a one-year extension to more than 4.2 million people whose current individual policies are being canceled by insurers to make way for more comprehensive coverage under the law. This move by the White House was intended to smooth a disruption for which his administration completely failed to plan.
But it also invited unintended consequences, showing how easily the law's complicated framework can start to come loose.
State insurance commissioners warned that the president's solution would undermine a central goal of the law, the creation of one big insurance pool in each state for people who don't have access to coverage on their jobs. Fracturing that market could lead to higher future premiums for people buying coverage through the law's new insurance exchanges, which offer government-subsidized private insurance.
That Obama is willing to take such a gamble could make it harder for him to beat back demands for other changes down the line.
On the cancellations front, the president seems unlikely to break through. He may yet battle to a political draw.
Obama realizes it's on him to try to turn things around, and quickly. In the first couple of weeks after the website debacle, Obama played the sidelines role of "Reassurer-in-Chief." Now he's on the field, trying to redeem himself.
"I'm somebody who, if I fumbled the ball, I'm going to wait until I get the next play, and then I'm going to try to run as hard as I can and do right by the team," Obama said Thursday at a news conference.
Making sure the website is running a lot better by the end of the month may be his best chance for a game-changing play.
Although only 26,794 people signed up in health plans through the federal site the first month of open enrollment, 993,635 applied for coverage and were waiting to finalize decisions. For many it took hours of persistence, dealing with frozen screens and error messages. When states running their own sites are included, a total of 1.5 million individuals have applied.
The law's supporters believe that's evidence of pent-up demand, and so far the insurance industry agrees. Public criticism of the administration by industry leaders has been minimal, even though insurers also have been on the receiving end of the website problems. Compounding the lower-than-expected sign-ups, much of the customer data they got was incomplete, duplicative or garbled.
Insurers, eager for the new business expanded coverage would bring, are pressing the administration to clear a route for them to sign up customers directly. Such workarounds may put Obama back on track toward his goal of signing up 7 million people for 2014. Medicaid expansion, the other arm of the law's push to cover the uninsured, signed up 396,000 people last month, a promising start.
With the website troubles, a national effort to promote insurance enrollments has been dialed down. Groups ranging from liberal activists and civic clubs to health promoters were mobilized and waiting. But there was little they could do. Advertising campaigns have been postponed. As the year-end holidays approach, both volunteers and the people they would be trying to reach have other priorities.
Whether enthusiasm among the rank-and-file supporters of the law will come surging back is one of the big unknowns for a president who has acknowledged the need to restore his credibility on health care.
"I think people have lost confidence in the ability of this working," said Kansas Insurance Commissioner Sandy Praeger. "And we've still got the anti-Obamacare folks out there taking full advantage." Praeger is a Republican who believes her state should have helped implement the law.
Skittishness among supporters was evident in the 39 House Democrats who Friday bolted their party to vote for Republican legislation on cancellations, ignoring Obama's veto threat.
Politics is not the only consideration.
The people who are signing up now are likely to be those with unmet medical needs. Younger, healthier customers probably don't see much reason to spend their time tangling with the website. To hold down costs, the law aims for a mix that includes a hefty proportion of younger enrollees whose medical expenses are low.
"Everybody said the website would be up and running the first day," said Praeger. "The longer it takes, the more people are going to question whether this is going to work."
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