The justices, who will rule by July, could permit Jones' case to move ahead promptly or suspend it until Clinton becomes a private citizen in 2001. She is seeking $700,000 from Clinton for sexual harassment, defamation and infliction of emotional distress.
Or the court could permit only pretrial preparations now, delaying the trial itself until 2001. Such a ruling could compel Clinton to answer pretrial questions under oath.
Such as: Did he expose himself to Paula Jones and request oral sex, as she has alleged? Did he regularly use state troopers to procure women, as some enemies in Arkansas have charged?
The questions and answers, even if taken in private, might be leaked to the news media.
Clinton, for his part, has made no statements about what happened between him and Jones, although his lawyer has said ``the incident did not occur.'' Clinton has spent an estimated $1.5 million in his defense.
On Friday, he was asked whether the Supreme Court hearing would cause him difficulty.
``I don't have any control over what anyone else does,'' Clinton said. ``I can only control what I do. It's not going to cause me any difficulty, because I'm going to do my job here.''
The case before the justices, Clinton v. Jones, asks whether the president's job is so unique, time-consuming and vital to the nation that the courts may not force him to defend himself in an ordinary civil suit while in office.
A related question is whether a judge could order a president to respond to questions, meet court deadlines, and appear for trial without violating the fundamental constitutional principle that forbids one branch of government from interfering with the independence of another.
A federal appeals panel ruled, 2-1, that the case could proceed without delay. The judges in the majority, both appointees of President Ronald Reagan, said Clinton was not constitutionally immune from the Jones suit and would not be inconvenienced by it.
They said that, if the case were to interfere with Clinton's duties, he could request more time, delays or altered schedules. They noted that many presidents found time to give testimony in court proceedings.
But Robert Bennett, the Washington lawyer who will argue the case for Clinton, has said that, with exceptions only for extraordinary circumstances, an incumbent president should not be forced ``to submit, as a defendant, to a civil-damages action directed at him personally.''
Otherwise, a president would become a target of suits filed by political enemies, publicity-seekers, or exploiters eager for a quick settlement, Bennett said.
Speaking yesterday on ABC's This Week, Joseph Cammarata, one of Jones' lawyers, said nothing in the Constitution or in law says a president can avoid lawsuits for actions he took as a private citizen, before he was elected to the White House.
``If you believe the [argument of the] president, then we have a monarchy. We have a king,'' he said.
Former White House counsel Lloyd Cutler, appearing on CBS' Face the Nation, said a president might be taken to court for civil cases where claims are made of irreparable injury such as in a divorce or failure to pay child support. But Jones, he said, makes no such claim, and her case should be deferred.
Legal researchers have found a paucity of personal suits against presidents. Only Theodore Roosevelt, Harry Truman and John Kennedy were sued for nonpresidential acts. But those suits, unlike Jones' complaint against Clinton, were filed before the defendants became presidents. Two were dismissed, and the third - against Kennedy - was settled.
Attorney Gilbert K. Davis, who represents Jones, will argue that the nation's affairs will not suffer if Clinton is required to participate in what Davis describes as ``a very simple dispute about what happened in a very short encounter between two people in a room.''
But to create a special personal privilege for a president would ``violate the precept that no man in this country is so high that he is above the law,'' Davis said.
Jones, now 30 and living in California with her husband and two children, has said she does not plan to attend the Supreme Court hearing today.
Most early media accounts portrayed Jones as a curvaceous, provocatively dressed woman of loose morals who posed almost nude for a boyfriend and was eager for money and fame, implying she was not to be believed.
Critics noted that her suit wasn't filed until nearly three years after the alleged incident and two days before the legal time limit was to run out. She became a target of gossip and late-night ridicule.
Then, in the November edition of The American Lawyer magazine, journalist Stuart Taylor dug into the case and found Jones' evidence to be ``highly persuasive.'' He reported that friends and relatives said she had told them essentially the same story of her meeting with Clinton soon after it allegedly occurred.
Taylor said two of Jones' friends recalled for him ``how an extremely upset Jones had told one of them within 10 minutes of the event, and the other within 90 minutes, that Clinton had suddenly exposed himself and demanded oral sex after Jones had rebuffed his efforts to grope her.''
Taylor wrote that he found Jones' evidence against Clinton stronger than Anita Hill's 1991 sexual-harassment claim against Clarence Thomas, who now is a Supreme Court justice.
Women's-rights groups that rallied behind Hill and attacked the conservative Thomas have declined to support Jones' case against the Democratic President.
Newsweek magazine put Jones on its cover last week, saying it too had concluded that her complaint should be taken seriously.
The Supreme Court has no precedent dealing directly with suits arising from an incumbent president's non-official acts, regardless of whether those acts occurred before or after he took office.
In 1982, the court did rule, 5-4, that a president is immune from suits related to his official acts. The court freed President Richard M. Nixon of a suit by a government whistle-blower, H. Ernest Fitzgerald, who charged that Nixon had fired him illegally for disclosing Air Force cost overruns.
Nevertheless, Acting U.S. Solicitor General Walter Dellinger, representing the government, will argue that the court's Nixon decision ``makes clear'' that a president's unimpaired performance of his duties trumps a private litigant's quest for civil damages.
But Davis, the lawyer for Jones, said the basic rationale behind the Nixon ruling - that making presidents vulnerable to suits would distort their presidential actions - is missing from the current case.
A group of law professors, siding with Clinton, said a secondary rationale favors the president. In the Nixon case, the Supreme Court sought ``to prevent the distraction from duty'' that would result from ``any litigation against the president.''
Another group of professors, backing Jones, said granting Clinton temporary immunity from civil suits would allow presidents to default on their mortgages and ``prevent a president's spouse from seeking a divorce and child custody.''