WASHINGTON -- Some presidents are handed the chance to remake the Supreme Court for a generation, if enough justices leave. Others wait in vain to make even one appointment.

President Barack Obama took office with a strong prospect that his first four years in office could bring two or more openings on the high court, though he may well be replacing aging liberal justices with younger ones.

Barring the unexpected, the court's balance of power -- four on the left, four on the right, one in the middle leaning right -- is not likely to change significantly.

Word of Justice Ruth Bader Ginsburg's illness on Thursday, just two weeks after Obama's inauguration, set off an inevitable round of speculation about whether she will have to retire sooner than she would wish -- and whom Obama might tap as her successor.

Chances are, Obama's first appointment will be a woman -- especially if it's to take the place of Ginsburg, the only woman on the court. And, like Ginsburg, she will be liberal leaning.

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Like every sitting justice, she also probably will be a federal appeals court judge. Obama has a number of options along those lines, including these five:

— Judge Diane Wood of the 7th U.S. Circuit Court of Appeals in Chicago.

— Judge Kim McLane Wardlaw of the 9th U.S. Circuit Court of Appeals in San Francisco.

— Judge Sonia Sotomayor of the 2nd U.S. Circuit Court of Appeals in New York.

— Pam Karlan, a law professor at Stanford University.

— Judge Margaret McKeown of the 9th Circuit in San Francisco.

Either Wardlaw or Sotomayor would be the court's first Hispanic justice.

Other court watchers have mentioned Elena Kagan, the former Harvard Law School dean whom Obama has nominated as solicitor general, Michigan Gov. Jennifer Granholm and Georgia Supreme Court Chief Justice Leah Sears.

The calculations would change, but only slightly, if Ginsburg's is not the first retirement. The president still would face strong pressure to name a woman or a minority or both.

Pancreatic cancer is a serious disease, with poor rates of long-term survival. But Ginsburg's doctors believe they found her growth early, which would boost her chance for recovery.

Plus, Ginsburg's diminutive appearance belies her toughness. She fought colon cancer nine years ago without missing a day in court.

No one on the court has signaled that a retirement is imminent, not even 88-year-old John Paul Stevens. Five justices are at least 70 and a sixth, David Souter, will turn 70 in September.

The three youngest are all conservatives -- Chief Justice John Roberts, 54, Samuel Alito, 58, and Clarence Thomas, 60. Roberts and Alito were appointed by President George W. Bush.

Roberts took over for like-minded William Rehnquist, whom Roberts once served as a law clerk. Bush's selection of Alito to replace Sandra Day O'Connor, the court's first woman, nudged the balance to the right.

Obama would have the opportunity to move the court to the left if one of the two older conservatives, Antonin Scalia or Anthony Kennedy, were to step down.

Kennedy is far less a doctrinaire conservative than the others, having joined his more liberal colleagues in recent years on cases involving gay sex, Guantanamo detainees and global warming.

The new president can only wonder at this point whether he will follow Bill Clinton and George H.W. Bush, who each filled two vacancies in their first four years. Actuarial tables suggest he will avoid the fate of Jimmy Carter, who had no high court nominees in his one term.

Obama might dream of the numbers rolled up by Richard Nixon, who named four justices in his first three years in office. But justices get lifetime tenure and no president can guarantee his picks will turn out the way he hopes.

Three Nixon appointees were part of the 8-0 vote by which the Supreme Court ruled in 1974 that he had to turn over audio tapes of Oval Office conversations to the Watergate special prosecutor. One of those justices, Harry Blackmun, was considered a staunch conservative when Nixon appointed him in 1970 but the court's most liberal when he retired in 1994.