President Bush's choice for Chief Justice of the United States, Judge John Roberts, appears on track to be confirmed by the Senate in time for the next Supreme Court session that begins on October 3. Some lawmakers from both parties are now focusing on who will be nominated to take the place of retiring Justice Sandra Day O'Connor.
So far, the president has given few hints about whom he might nominate to replace Justice O'Connor.
"As a result of my decision to nominate Judge Roberts to be chief justice, I also have the responsibility to submit a new nominee to follow Justice Sandra Day O'Connor," he said. "I will do so in a timely manner."
Opposition Democrats want a moderate who will follow Justice O'Connor's lead as a centrist on the Supreme Court.
"I would hope that he would give [propose] a nominee that would unite both Democrats and Republicans because that would be important as a swing vote in the Supreme Court," said Patrick Leahy, Democratic Senator from Vermont,on the CBS program, Face the Nation.
Some Republicans hold a similar view. Pennsylvania Republican Arlen Specter chairs the Senate Judiciary Committee, the panel that holds confirmation hearings for judicial appointments.
"I would like to hear that the president is going to maintain balance, that you have a very evenly divided court and that there are a great many issues that many people are worried about on both sides of the political spectrum," he said.
Many other Republicans are urging the president to stand by his campaign pledge to nominate a justice in the mold of the two leading conservatives on the court, Justices Antonin Scalia and Clarence Thomas.
Legal and political analysts see the president's choice on a successor for Justice O'Connor as potentially more divisive than his decision to nominate John Roberts to succeed the late Chief Justice William Rehnquist.
Judge Roberts is seen by many as a mainstream conservative in the mold of Chief Justice Rehnquist and most experts predict little change on the high court as a result.
But if the president were to nominate a strong conservative to replace the more moderate Justice O'Connor, that could have a profound impact on the court for years to come.
"The more critical seat from the standpoint of the court's lineup is Justice O'Connor's seat," said A.E. Dick Howard, a constitutional law expert at the University of Virginia, who spoke to VOA's Focus program. "She was a conservative, but a more moderate conservative. She was often the critical vote in five to four cases. She played a role of somewhat pulling the court to the center."
There have also been calls for the president to appoint a woman or a minority to take the place of Justice O'Connor. She became the first woman appointed to the Supreme Court by President Ronald Reagan in 1981.
"But I do think there is considerable political pressure for the president to reach out to a minority or a female in making this selection," said Pat Woodward, who is with the Republican National Lawyers Association. He appeared on VOA's Encounter program.
The president has hinted he would like to appoint the first Hispanic to the Supreme Court. The only minority justice at present is Justice Clarence Thomas, an African-American.
Some Democrats have warned that nominating a strident conservative for the high court could bring about a filibuster in the Senate, a parliamentary tactic in which a minority of senators tries to prevent a confirmation vote by the full Senate.
Aaron Epstein is a long-time Supreme Court analyst who was on VOA's Encounter program.
"But if he goes with his right-wing constituency and appoints a real right-wing ideologue, then I think he is going to be in for a lot of trouble and then we may see that filibuster we have been talking about," he said.
Most legal and political analysts expect the president to nominate a successor for Justice O'Connor once Judge Roberts is confirmed by the Senate as the next chief justice.