Predicting the outcome of the health care case is hard, because it is both surpassingly important and quite idiosyncratic.

The law, Patient Protection and Affordable Care Act, sets out to eliminate the United States’ status as the only rich country without almost universal health care. Mr. Obama’s aides compare its significance to that of Medicare or Social Security, while Republican leaders say it helps move the country dangerously close to European-style big government.

The court that will hear the health care case is in some ways as extraordinary as the case itself.

For the first time since at least 1953, when Chief Justice Earl Warren joined the court, the justices are divided along not only ideological but also partisan lines: its five more conservative members were all appointed by Republican presidents and its four more liberal members by Democrats.

Add to that the conventional wisdom about which votes in the health care case are fixed in concrete: the four justices appointed by Democrats are thought certain to vote to uphold the law, and Justice Clarence Thomas, appointed by the elder George Bush, is believed to be a sure vote to strike it down.

The consensus among scholars and Supreme Court practitioners is that Chief Justice Roberts is unlikely to add the fifth vote to those of the four justices in the court’s liberal wing to uphold the law. But he is said to be quite likely to provide a sixth vote should one of the other more conservative justices decide to join the court’s four more liberal members.

Either way, then, the chief justice is likely to be in the majority. Indeed, in the last two terms Chief Justice Roberts has been in the majority at least 90 percent of the time, a distinction he shares with only Justice Anthony M. Kennedy, the court’s swing justice.

Should a closely divided court strike down the health care law, the decision will call to mind Bush v. Gore in 2000 and Citizens United v. Federal Election Commission in 2010. They were 5-to-4 rulings decided along ideological lines, but there were Republican appointees on both sides.