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.

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.