Supreme Court: Who's Next?

(CBS)  When John Roberts begins his first term as chief justice of the United States on Monday, he'll be leading a Supreme Court sharply divided over many issues, and one with a pivotal retiring justice.

As CBS News Senior White House Correspondent Bill Plante

explains (video)

, the new justice will be filling the spot left by Sandra Day O'Connor, who's been the swing vote in many 5-4 decisions.

And the pressure, Plante says, is on President Bush from both sides.

Democratic Sen. Chuck Schumer of New York summed it up when he asked, "Do they consider it the right thing to do to reach out to the middle, or do they sort of batten down the hatches and firm up the hard base on the other side?"

Democrats are threatening a filibuster if the president nominates someone they consider extreme, Plante says.

Conservatives want Mr. Bush to keep his promise and pick someone in the mold of justices Antonin Scalia and Clarence Thomas.

"The president does not have any obligation to make a consensus appointment here," says Jay Sekulow of the American Center for Law and Justice. "What the president's obligation is, is to pick a judicial conservative, and I believe that's what he's gonna do."

Possible candidates, Plante says, include Judge Priscilla Owen, whom Democrats say would trigger a filibuster; White House counsel Harriet Miers, who has no judicial experience; Attorney General Alberto Gonzales, another close friend of the president; and former Deputy Attorney General Larry Thompson.

Plante says the president probably won't make his choice known until next week, but it is the key to the future of the court.

"And Mr. Bush has to decide," Plante says, "does he pick someone who will set off a war with Democrats, and maybe take the court in a more conservative direction, or does he do what he did with Chief Justice Roberts," who appealed to the middle?

When he was sworn in Thursday, Roberts said, "Every generation in its turn must accept the responsibility of supporting and defending the Constitution, and bearing true faith and allegiance to it. That is the oath that I just took."

Now, Plante says, the nation waits for Mr. Bush's next nominee, who may have a far more difficult time getting Senate approval.