The court scheduled five and a half hours of arguments instead of the usual one, a testament to the importance of the case, and the court’s ruling a few months later will present opportunities and challenges for the presidential contenders as well as for candidates in the battle for control of Congress.

It is hardly clear, for instance, that a Supreme Court ruling upholding the law would help only Mr. Obama, as opponents of the law might redouble their efforts to elect candidates committed to repealing it. And a decision striking down the law might allow Mr. Obama to court voters unhappy with the Supreme Court’s decisions as he did in cases like Citizens United, which allowed unlimited campaign spending from corporations and unions. Appeals from three courts had been vying for the justices’ attention, presenting an array of issues beyond the central one of whether Congress has the constitutional power to require people to purchase health insurance or face a penalty through the so-called individual mandate.

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The Supreme Court agreed to hear appeals from just one decision, from the United States Court of Appeals for the 11th Circuit, in Atlanta , the only one so far striking down the mandate. The decision, from a divided three-judge panel, said the mandate overstepped Congressional authority and could not be justified by the constitutional power “to regulate commerce” or “to lay and collect taxes .”

The appeals court went no further, though, severing the mandate from the rest of the law.

On Monday, the justices agreed to decide not only whether the mandate is constitutional but also, if it is not, how much of the balance of the law, the Patient Protection and Affordable Care Act, must fall along with it.

But even the Obama administration has said that the mandate is “absolutely intertwined” with two other provisions — one forbidding insurers to turn away applicants, and the other barring them from taking account of pre-existing conditions.

In a statement issued soon after the decision, the administration reaffirmed its position that the Constitution permitted Congress to enact the mandate.

“We know the Affordable Care Act is constitutional and are confident the Supreme Court will agree,” said Dan Pfeiffer , the White House communications director.

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Pam Bondi, Florida ’s attorney general, said she welcomed the court’s prompt action in agreeing to review the 11th Circuit’s decision, in which her state was the lead plaintiff.

“Throughout this case,” Ms. Bondi said, “we have urged swift judicial resolution because of the unprecedented threat that the individual mandate poses to the liberty of Americans simply because they live in this country.”

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Representative Nancy Pelosi of California , the House Democratic leader, said a decision upholding the law would mean that “Americans will benefit from lower health care costs and greater access to high-quality medical care.”

But leading opponents of the law said they were confident they would triumph.

“It is high time for the high court to strike down this unconstitutional, unworkable and unpopular law,” said Randy E. Barnett, a law professor at Georgetown.

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The 11th Circuit did rule against Florida and the other states on one of their other central arguments, rejecting a challenge to the law’s expansion of the Medicaid program.

The Supreme Court also agreed to hear an appeal from that ruling.

The states, represented by Paul D. Clement, a former United States solicitor general, argued that Congress had exceeded its constitutional authority by expanding the eligibility and coverage thresholds that states must adopt to remain eligible to participate in Medicaid.

The problem, Mr. Clement wrote, was that “Congress did not tie its new conditions only to those additional federal funds made newly available under” the Affordable Care Act. “It instead made the new terms a condition of continued participation in Medicaid, thereby threatening each state with the loss of all federal Medicaid funds — on average, more than a billion dollars per year — unless it adopts the act’s substantial expansions of state obligations.”

The justices also said they would consider an intriguing threshold issue that could conceivably postpone any definitive ruling on the mandate until 2015.

In September, a divided three-judge panel of the United States Court of Appeals for the Fourth Circuit, in Richmond , Va., ruled that it was premature to decide the case in light of the Anti-Injunction Act, a federal law that bars suits “for the purpose of restraining the assessment or collection of any tax.” The Supreme Court had interpreted the term “tax” very broadly for purposes of the law.

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If the Fourth Circuit ruling is correct, individuals may not challenge the individual mandate until the first penalty is due in April 2015.

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On Nov. 8, a dissenting judge on the United States Court of Appeals for the District of Columbia Circuit also endorsed that position.

The administration had initially pressed but later abandoned the argument.

In the Supreme Court, the Justice Department suggested that the court consider the issue and perhaps appoint a lawyer to present arguments in favor of it, as the court occasionally does when the parties agree on a significant issue that could alter the outcome of the eventual decision. The court did not say on Monday whether it would make such an appointment, but the prospect seems likely.

The justices will hear two hours of argument on whether Congress overstepped its constitutional authority, 90 minutes on whether the mandate may be severed from the balance of the law if Congress did go too far, and an hour each on the Medicaid and Anti-Injunction Act questions.

In all, the Supreme Court agreed to hear three appeals, two from challengers to the law and a third from the Obama administration.

The appeals involving the 26 states is known as Florida v. Department of Health and Human Services , No. 11-400. A second challenge, from a business group and two individuals, is called National Federation of Independent Business v. Sebelius, No. 11-393. The federal government’s appeal is Department of Health and Human Services v. Florida, No. 11-398.

There was no indication in Monday’s order that any of the justices had decided to disqualify themselves from the case. Such a notation is customary when justices have decided not to participate.