Supreme Court Chief Justice William Rehnquist (search) kept people guessing last week about whether he would hand in his resignation, but the big question facing President Bush is what to do with the vacancy created by Justice Sandra Day O'Connor's (search) retirement.

Many liberals and conservatives agree that O'Connor's seat on the court should be reserved for a woman — so long as she is the right kind of woman.

"Let's be real. What we'd like is a person who's a woman, but also a woman like Sandra Day O'Connor, who will not go backward on women's rights," said Eleanor Smeal, president of the Feminist Majority Foundation.

"Yes, I would love a woman. I would love a woman in the mode of a is there a 'Nina Scalia' in the house that's available?" said former deputy assistant attorney general Victoria Toensing.

A female version of Justice Antonin Scalia (search) is unlikely to be found, and court-watchers may not even be able to find another O'Connor.

Less likely, say observers, is the chance of finding a combination of the two.

"I don't think there's anyone who can be a man or woman for all seasons in American law right now, because you cannot be Sandra Day O'Connor and Antonin Scalia at the same time. They are mutually inconsistent," said Eddie Lazarus, a partner with Akin Gump law firm who clerked for former Justice Harry Blackmun (search).

Sen. Arlen Specter (search), R-Pa., chairman of the Senate Judiciary Committee, is on the record saying that the court should have no fewer than two women.

Women's groups on the left agree that they want four or five women on the high court so long as none of them is conservative.

"We want one who is going to further a woman's rights, not one who is going to slam the door in other women's faces. So, basically, we don't think that's too much to ask," Smeal said.

For some conservatives, like Toensing, ideology trumps gender.

"I would love a clear-thinking conservative woman on the court, but given the choice between one or the other, it's important that we have good justices on the Supreme Court," she said.

In the Democratic weekly radio address on Saturday, Senate Minority Leader Harry Reid (search) of Nevada also seemed less concerned with gender than ideology.

"As the first woman to serve as a Supreme Court Justice, she blazed a trail that hopefully many will follow. Justice O'Connor decided cases the old fashioned way — based on law, not politics," Reid said.

"I hope that President Bush and the Senate can work together to nominate and confirm a justice who lives up to that word: Someone who can build on our national consensus on important issues; someone with a deep respect for the Constitution; and someone with enough common sense to know that Supreme Court justices should not impose a narrow partisan ideology, but make rulings with an open mind and a big heart."

Lazarus said he doubts the president is under any pressure to replace O'Connor with a woman.

"I think President Bush has already demonstrated that he's committed to have women in very high positions of government. Obviously, (Secretary of State) Condi Rice is the prominent example, but there are many others. So I don't think he is under any political pressure to show that he believes that women can hold these posts," he said.

O'Connor helped President Reagan achieve two goals — making history by being the first president to appoint a woman to the court, and adding a conservative to the bench.

But as O'Connor's career proved her to be conservative in the early 1980s, she may not be perceived that way 20 years later.

That's why the White House says it is looking for intellectual, judicial and ethical qualifications over other considerations, whether political or symbolic.

Click in the box near the top of the story to watch a report by FOX News' Major Garrett.