News media packed the court Monday morning for its most closely watched case in years, and dozens of people lined up for as long as 2½ days to get seats in the courtroom.

The most closely watched issue in the case is whether Congress exceeded its constitutional powers by passing a mandate requiring most Americans to carry health insurance or pay a penalty. But to rule on that issue, the court first has to conclude that plaintiffs are allowed to challenge the mandate now, before the penalties go into effect in 2014.

Most lower courts decided that the lawsuits can proceed. But one federal appeals court, in Richmond, Va., reached a contrary conclusion. That court relied on the Anti-Injunction Act, a federal law that prohibits pre-enforcement challenges to tax laws in most circumstances. The Richmond court said the insurance-mandate penalties amount to a type of tax that can only be challenged after it is collected, rather than before.

Because none of the parties in the case support that position, the Supreme Court had to appoint a lawyer to argue it. That lawyer, Robert A. Long of Covington & Burling LLP, was first up in Monday's scheduled 90-minute argument. Later in the session, lawyers for the federal government and the law's challengers were set to argue that the justices don't have to wait to decide the important constitutional issues.

The Supreme Court has scheduled six hours of oral arguments on the health-care law. The main attraction comes Tuesday, when the court considers the constitutionality of the insurance mandate.

On Wednesday, the court will consider whether the rest of the health-care overhaul can remain intact if the insurance mandate is ruled invalid. The law's challengers are seeking to void the entire law, while the Obama administration argues that most of the law's provisions aren't connected to the mandate and should remain in place even if the insurance requirement is struck down. The court will also consider 26 states' legal attack against the health-care law's expansion of Medicaid, a federal-state partnership that provides health care to low-income Americans. Lower courts ruled for the Obama administration on this issue.

A decision in the case is expected by the end of June.

In taking up the case, the Supreme Court wades into an issue that not only could sway this fall's elections but also could help define for generations what Congress is and isn't entitled to do.

The Obama administration and its allies say the court must uphold the law to ensure that Congress can tackle national problems by employing comprehensive solutions. In jeopardy, critics say, is the fundamental American idea that the federal government should be restricted in what it can require of citizens.

"This case will be a tremendous opportunity to reaffirm that Congress is a legislature of limited powers," said Randy Barnett, a Georgetown University law professor who is helping the challengers.

On the eve of the court arguments, the case was being cast in political tones. White House senior adviser David Plouffe said on NBC's "Meet the Press" Sunday he was confident the justices would uphold the law, saying that Americans were already benefiting from elements of the plan. But Sen. Lindsey Graham (R., S.C.) said the health law would be a top issue for the eventual Republican nominee.

"From a political point of view, this is probably the centerpiece of the debate in the fall—the proper role of government," he said on CNN's "State of the Union."

Harvard University law professor Laurence Tribe, who taught both Chief Justice John Roberts and Mr. Obama and was an Obama Justice Department official, said opponents are asking the court to erase the flexibility the Constitution's framers gave Congress. If the court struck down Mr. Obama's law, said Mr. Tribe, it would implicate "virtually every major piece of federal legislation enacted over the past several decades, and many laws now in the pipeline"—including proposals favored by conservatives.

Opponents—led by former George W. Bush Solicitor General Paul Clement, representing 26 Republican-led states—say the Constitution's clause allowing Congress to regulate interstate commerce doesn't apply here. They say Congress is creating the very "commerce" it wishes to regulate by compelling consumers to purchase insurance.

Georgetown's Mr. Barnett said the court could strike down the mandate using narrow language intended to avoid broader implications. Challengers merely want the court to say that "Congress has never gone here before, and it can't go here again," he said.

To date, the government has the most points on the scoreboard: Three federal appeals courts have rejected challenges to the Affordable Care Act, while one has struck down the individual mandate but upheld the rest of the law. Moreover, the government enters the court with four likely votes lined up, those of liberal Justices Ruth Bader Ginsburg, Stephen Breyer, Sonia Sotomayor and Elena Kagan, whose prior writings suggest they will view the overhaul as within congressional discretion.

To win, the challengers must secure all five conservatives. Based on his prior opinions, Justice Clarence Thomas seems virtually certain to vote against the mandate. The records of the other four, however, are sufficiently ambiguous as to make their votes more difficult to predict. Of the justices considered persuadable, Justice Anthony Kennedy may be the biggest target, as his opinions were cited in the two sides' briefs far more than those of any other justice.