The odds that the court would strike down the mandate appeared higher on Tuesday after a key justice who often holds the tie-breaking vote on the nine-member body appeared openly skeptical about its constitutionality.
Signed into law in 2010, the Affordable Care Act has been touted as a Democratic dream of generations, extending health care coverage to 32 million Americans who are currently uninsured.
But Republicans and 26 states led by Florida have attacked it as an assault on individual liberty, plunging the top US court into perhaps its biggest case since it decided the 2000 presidential election in favor of George W. Bush.
In a packed hearing on Tuesday, the nine justices went to the heart of the law the so-called individual mandate requiring all Americans to maintain minimum adequate health insurance.
Justice Anthony Kennedy, widely considered a swing voter, joined the court's conservative wing in suggesting that it could fundamentally alter the relationship between the government and individuals by forcing Americans to buy insurance they did not want.
"When you are changing the relation of the individual to the government in this, what we can stipulate is, I think, a unique way, do you not have a heavy burden of justification to show authorization under the constitution?" he said.
With that question hanging, the justices were to devote part of a third and final day to considering whether the whole law should be struck down if the individual mandate does not survive.
They also will take up another provision of the law that makes more Americans eligible for Medicaid the public insurance program for the poor which the states have challenged as an infringement on their powers.
The health care law Obama's signature domestic achievement encompasses the most ambitious reform of the troubled US health care system in decades.
It sets forth wide-ranging incentives and penalties to expand nationwide health care coverage, fining large firms that do not offer employees adequate insurance while offering subsidies to small businesses to blunt the cost.
The government and the states challenging the law have all argued that the requirement that individuals buy health insurance or pay fines is core to the reform's viability.
Lower courts have differed, however, on whether the law as a whole would be doomed without the requirement.
A federal appeals court that found the individual mandate unconstitutional also concluded that "the lion's share of the act has nothing to do with private insurance, much less the mandate that individuals buy insurance."
Among the provisions of the law that could survive, it said, were those requiring insurers to enroll all applicants and prohibiting them from denying coverage to people with pre-existing medical conditions.