Eric Lichtblau / New York Times News Service

WASHINGTON — Justice Clarence Thomas likens all the outside political pressure that the Supreme Court is facing over its review of the Obama administration’s sweeping health care law to the distraction faced by a free-throw shooter confronted with fans waving wildly behind the basket. Neither, in his view, has much impact in the end.

“Why do you think they’re never distracted? They’re focusing on the rim, right?” Thomas said when asked at a forum two weeks ago about the pressures of the health care case. “That’s the same thing here,” he said. “You stay focused on what you’re supposed to do. All that other stuff is just noise.”

With three days of arguments set for this week, the justices will need the steely nerves of a clutch free-throw shooter to block out the noise surrounding a case that has generated perhaps the most intense outside lobbying campaign that the court has ever seen.

The Chamber of Commerce, which has helped lead opposition to the health plan, has been hosting moot court sessions to prep lawyers involved in the case. Advocates on all sides of the issues are planning rallies. Many groups, like the American Constitution Society, liberal backers of the law and of Congress’ power to regulate commerce, are setting up war rooms and daily briefings on the Supreme Court steps to provide near-instant readouts on the oral arguments.

In all, groups involved in the debate have spent tens of millions of dollars in the last two years to steer the political and legal debate. And a record number of organizations — 136 so far — have filed amicus or “friend of the court” briefs, densely packed with historical citations and legal arguments, to urge the court to either strike down or uphold the sweeping health care law crafted by the Obama administration.

“Whenever you see a blockbuster case, we see the different groups coming out,” said Anthony Franze, a lawyer who co-authored a study of amicus briefs. “And this is the blockbuster of blockbusters.”

With the start of arguments this week, the lobbying efforts move from Congress squarely to the Supreme Court, which has found itself drawn increasingly into politically charged cases in recent years, including its intervention in the 2000 Florida recount in Bush v. Gore; its rulings limiting the sweep of executive power in Guantánamo Bay; and its remaking of campaign finance law in the 2010 Citizens United ruling.

Lobbyists and lawyers with a stake in the case will be giving near-instant analysis for their clients and for reporters.

Proponents of the sweeping 2010 law have also developed “talking points” to emphasize the potential harm if the law is thrown out, including the reduction in coverage for those with pre-existing conditions and for young adults who wish to remain on their parents’ policies.

The groups filing friend-of-the-court briefs with their views of the law include not only the usual heavy hitters like the chamber, AARP and virtually every major health care association, but also obscure groups rarely if ever involved in Supreme Court cases.

“We don’t expect to be even a blip on the court’s radar, except to maybe count up the ‘for’ and ‘against,’ ” said Quentin Rhoades, a lawyer for the Montana Shooting Sports Association, which filed a 26-page brief opposing the law.

Prize-winning economists are wading into the debate with briefs that offer clashing views of the economic benefits and harms that they believe the health care law brings.

Will lobbying have effect?

But does the cajoling have any real impact on the court’s decisions?

At least in the case of the formal amicus briefs filed with the court, research suggests that, increasingly, the answer is yes.

A study published last year in The National Law Journal by Franze and R. Reeves Andersonfound the Supreme Court justices not only receiving more amicus briefs than ever before, but also citing them as support for their opinions far more often as well.

But the impact of less formal politicking — media coverage, rallies, protests, forums and other “noise,” as Thomas called it — is less clear.

In a speech last year in Kansas City, Justice Stephen Breyer said politics outside the court’s chambers should not — and generally does not — play a part in its deliberations.

Among the stories in the news media over the past few months were questions about whether he and Justice Elena Kagan could objectively consider the health care case because of their own personal and political connections.

Liberals in Congress and elsewhere say that Thomas’ objectivity is called into question by the consulting work that his wife, Ginny Thomas, has done with tea party groups in opposing the health care law.

Conservatives, meanwhile, assert that Kagan’s own impartiality could be compromised by her role as President Barack Obama’s first solicitor general during the start of the legal fight over the health care legislation.

Neither justice has indicated any hesitation to hear the case. And Chief Justice John Roberts has said that he has confidence in all his justices — who are not bound to follow the ethics guidelines that govern federal judges — to decide when they may want to remove themselves from a case because of a possible conflict. Bradley Joondeph, a law professor at Santa Clara University who has cataloged briefs in the case, said that while he saw no need for either justice’s recusal, he believes it is unrealistic to think the court could fully insulate itself from outside pressures.

“There’s no way for human beings to screen out the rest of the world on a decision like this,” Joondeph said. “This just sort of stands out as one of those cases where the institutional stature of the court is on the line.”