Calculating who will write the final decision of the Supreme Court’s term is a game that usually interests only a small band of lawyers, professors, reporters and politicos who obsess over the justices’ every footnote.

But this year, the likelihood that Chief Justice John G. Roberts Jr. is preparing the court’s judgment on President Obama’s health-care overhaul is worthy of headlines and a whirl of Internet spin.

Roberts’s questions at oral arguments are being consulted, his decisions in past cases are being reviewed, and the analysis is underway about whether he is preparing a life preserver or a stake for the Affordable Care Act.

The first Monday in October and the last week of June, the bookends for each session, are always moments in the spotlight for the Supreme Court. But this is no ordinary time.

The court has rarely occupied so prominent a place in the public consciousness as now: deciding the constitutionality of a health-care plan that would touch every American, ruling on the president’s bitterly fought signature domestic achievement, issuing an opinion that will immediately affect election-year politics.

“More people have paid attention to this case than any other case in recent memory, probably with the exception of Bush v. Gore,” Paul D. Clement, who argued the case on behalf of the law’s challengers, told reporters last week.

But that ruling, which decided the 2000 presidential election, was an anomaly, an emergency that no doubt sealed the court’s reputation for many but was unlike its usual practice of briefing and argument and contemplation and opinion-writing.

Health care, Clement said, “is a case where everybody from ordinary citizens to reporters who are not used to covering the court are getting an education in how the court works.”

The main way it works, of course, is in secrecy, beyond public view and in a place unlike much of official Washington.

Television cameras are not allowed. The lucky spectators admitted to the courtroom are told to check their BlackBerrys at the door. Reporters are discouraged from using noisy cellphones, even in the press room. Ornate metal gates block the marble stairways that lead to the justices’ chambers.

Unlike many other institutions in this city, the court sticks to a sharp timetable — the decision will be delivered Thursday morning, shortly after 10 a.m. And unlike in the rest of leak-happy Washington, discretion is demanded above all else. The health-care case was probably decided soon after the court’s historic three days of hearings in March. But even now, only a few dozen court employees — half of whom are probably unhappy with the decision — know the outcome.

Clement, who was solicitor general under President George W. Bush, said people unfamiliar with the court, especially political reporters, cannot believe that the result has not been disclosed.

“The thing I’ve found most amusing is their complete inability to believe there will not be leaks,” Clement said. “They are so used to covering the other two branches of government that they just assume leaks are absolutely inevitable.”

Absent those, Monday’s gush of news from the court, on its penultimate day of decisions, provided much fodder.

When Justice Anthony M. Kennedy was announced as the author of the opinion on Arizona’s restrictive immigration law — the court’s second most significant case of the term — that provided a clue that Roberts would be writing the health-care ruling. Roberts and Kennedy are thought to hold the balance of power on the case, and it would be unlikely that Kennedy would write both.

The court delivered a split decision in the Arizona case, upholding the most controversial provision of the law with a sort of “we’ll be watching” warning and striking three others — and prompting immediate speculation. Could the ruling provide a template for a health-care compromise? Could the justices, for instance, strike the health-care law’s unpopular insurance mandate and still find a way to make the overhaul work?

Monday’s session provided another lesson for those who were there to witness it. The justices regularly declare themselves to be warm and caring colleagues, shaking hands before each session and proclaiming that harsh words are never spoken in their private conferences.

But things can look different on the bench. Justice Elena Kagan announced the court’s decision that states may not mandate life sentences without parole for juvenile killers. Then the justice to her immediate right, Samuel A. Alito Jr., was moved for the first time in his career on the court to object from the bench.

He dressed down the logic of the opinion — and its endorsement of what he called an elitist attitude — that overturned what he said should be a prerogative of the states.

Barbara Perry, a Supreme Court expert at the Miller Center at the University of Virginia, was in the audience. “You could just hear the emotion in his voice,” she said.

Kagan, the newest justice, had not quite mastered the art of staring impassively ahead.

There was more. Justice Antonin Scalia ripped the court’s immigration ruling, with an unexpected criticism of Obama’s decision to ease deportation of illegal immigrants who were brought to the country as children.

“The president has said the new program is ‘the right thing to do’ in light of Congress’s failure to pass the administration’s proposed revision of immigration laws,” Scalia said. “Perhaps it is, though Arizona may not think so.”

Perry thought it was a “gratuitous shot,” adding that she felt the same when Obama criticized the court during the State of the Union address in 2010.

A former Supreme Court fellow who worries about the institution, she is distressed by polls that show growing public dissatisfaction with the court and an increasing number of people who think its decisions are politically motivated.

“Whenever the court enters the political thicket, it does so at its own peril,” she said.

Later Monday, Perry attended a seminar for teachers at the court, and when she emerged, after the bustle and emotion of the morning, the place had returned to its natural state.

The marble halls were empty; all was quiet. Even the plaza outside was deserted, save for a couple of television reporters completing their stand-ups. Rain began to sprinkle, she said, and then they left, too.