It’s pressure cooker time at the Supreme Court.

With oral arguments over, the justices are holed up with their clerks churning out draft opinions in pending cases, with an internal deadline of June 1. Once the opinions are circulated to colleagues, draft dissents are supposed to be done by June 15, so the justices can close up shop for the summer by June 30. But this year, undeniably, the heat has been cranked up higher than usual. The intense scrutiny given to the health care and immigration cases has brought the anticipation to unprecedented levels.

“I’ve never seen a term in which so many members of the public are interested in what the Court is going to do,” said Lisa Blatt, head of Arnold & Porter’s Supreme Court and appellate practice.

“The justices know they are being watched,” said Elizabeth Papez, appellate partner at Winston & Strawn and a former clerk to Justice Clarence Thomas. That does not mean the justices will be “unduly influenced,” she is quick to add, but “it will make an already stressful time at the Court even more stressful.”

More than likely, no one is feeling the pressure more than Chief Justice John Roberts Jr., whose stewardship this term could shape his legacy — and the Court’s. He is also the traffic manager who has to shepherd all the Court’s pending cases to a smooth resolution.

Roberts took steps to ease the hectic pace at the Court in the weeks before its usual adjournment in late June. Only half as many cases were argued in April as usual, giving the justices fewer quick-turnaround decisions to write.

But still the cases have piled up. Twenty of the 72 cases the Court heard this term have yet to be decided, a typical percentage that will make for a busy next five weeks.

Health care and immigration are not the only issues that have constituencies eagerly awaiting action by the high court. Two key First Amendment cases may be giving justices heartburn at the writing stage.

One, FCC v. Fox Television Stations, is a test of the government’s broadcast indecency standards. Sidley Austin’s Carter Phillips, who argued against the Federal Communications Commission in Janu­ary, said the case is “almost certainly going to generate more than two opinions, which is what likely explains the delay.” The other free speech case is the closely watched U.S. v. Alvarez, which asked the Court to decide if Congress can make it a crime to lie about having won a military honor. It was argued on Feb. 22.

But those and other pending opinions are dwarfed by the enormity of the health care cases, argued in late March. Not only are the issues complex, but the consequences are far weightier than an ordinary challenge to an act of Congress.

Every day the Court deliberates, the behemoth health care law, which is being implemented in phases, affects more and more people. The future of a huge segment of the American economy is at stake. Striking down the law would “derail a train with millions of individuals and businesses on board,” said Ethan Rome of Health Care for America Now, a strong advocate of the law.

If the law is struck, it would be the first time since the New Deal that the Court has pulled the plug on such a major programmatic, service-providing law, said George Washington University Law School associate dean Alan Morrison.

That should not enter into the Court’s deliberations, said the Cato Institute’s Ilya Shapiro, a critic of the health law. “Even if millions benefit from some of Obamacare’s provisions, other millions suffer due to the legislation’s drain on our economy,” he said. “In any event, these considerations are irrelevant to the constitutional issues the Court is deciding.”

The health care law also has legions of opponents and supporters. So will the Court — or should it — take public opinion into account?

“I don’t think the Court should be reading polls,” said New York University School of Law professor Barry Friedman, author of a 2009 book on the interplay between the Court and public opinion. At the same time, he said, “the justices live on the same planet we do” and may be constrained to a degree by their perception of how popular or unpopular their decision will be.

Since the arguments, commentators have singled out Roberts as the key figure who may feel an institutional obligation to ensure that the Court is not viewed as a “political entity.” If he does, Papez said, now is when Roberts will play that role to the fullest.

He may be seeking compromise on some issues, leaving parts of the law in place and striking down others so as to achieve a 6-3 margin or higher. The severability issue — whether the entire health care law falls if the individual mandate is rejected — may be a focal point for negotiations.

“When they took their vote on the case rights after argument, there was no opinion in front of them,” Papez said. “Now that the opinions are circulating, the rubber meets the road.”

Tony Mauro can be contacted at tmauro@alm.com.