But the topic the justices take up first on Wednesday only comes into play if they first find that the insurance mandate violates the Constitution. If they do, then they will have to decide if the rest of the law stands or falls.
The states and the small business group opposing the law say the insurance requirement is central to the whole undertaking and should take the rest of the law down with it.
The administration argues that the only other provisions the court should kill in the event the mandate is stricken are insurance revisions that require insurers to cover people regardless of existing medical problems and limit how much they can charge in premiums based on a person's age or health.
The federal appeals court in Atlanta that struck down the insurance requirement said the rest of the law can remain in place, a position that will be argued by a private lawyer appointed by the justices, H. Bartow Farr III.
On Tuesday, the conservative justices sharply and repeatedly questioned the validity of the insurance mandate.
If the government can force people to buy health insurance, justices wanted to know, can it require people to buy burial insurance? Cellphones? Broccoli?
Audio and transcripts for Tuesday's court argument can be found here.
The court focused on whether the mandate for Americans to have insurance "is a step beyond what our cases allow," in the words of Justice Anthony Kennedy.
"Purchase insurance in this case, something else in the next case," Chief Justice John Roberts said.
But Kennedy, who is often the swing vote on cases that divide the justices along ideological lines, also said he recognized the magnitude of the nation's health care problems and seemed to suggest they would require a comprehensive solution.
And Roberts also spoke about the uniqueness of health care, which almost everyone uses at some point.
"Everybody is in this market, so that makes it very different than the market for cars or the other hypotheticals that you came up with, and all they're regulating is how you pay for it," Roberts said, paraphrasing the government's argument.
Kennedy and Roberts emerged as the apparent pivotal votes in the court's decision.
The law envisions that insurers will be able to accommodate older and sicker people without facing financial ruin because the insurance requirement will provide insurance companies with more premiums from healthy people to cover the increased costs of care.
"If the government can do this, what else can it not do?" Justice Antonin Scalia asked. He and Justice Samuel Alito appeared likely to join with Justice Clarence Thomas, the only justice to ask no questions, to vote to strike down the key provision of the overhaul. The four Democratic appointees seemed ready to vote to uphold it.
Kennedy at one point said that allowing the government mandate would "change the relationship" between the government and U.S. citizens.
"Do you not have a heavy burden of justification to show authorization under the Constitution" for the individual mandate? asked Kennedy.
At another point, however, he also acknowledged the complexity of resolving the issue of paying for America's health care needs.
"I think it is true that if most questions in life are matters of degree ... the young person who is uninsured is uniquely proximately very close to affecting the rates of insurance and the costs of providing medical care in a way that is not true in other industries. That's my concern in the case," Kennedy said.
Justice Ruth Bader Ginsburg said she found the debate over health care similar to an earlier era's argument about the Social Security retirement system. How could Congress be able to compel younger workers to contribute to Social Security but be limited in its ability to address health care? she wondered.
"There's something very odd about that, that the government can take over the whole thing and we all say, Oh, yes, that's fine, but if the government wants to preserve private insurers, it can't do that," she said.