After a breakfast meeting with key Senate leaders at the White House Wednesday, President Bush was keeping close to his vest his choice of a replacement for Sandra Day O'Connor (search) on the U.S. Supreme Court.

Meanwhile, Senate Judiciary Committee Chairman Arlen Specter (search), R-Pa., said he anticipates that the upcoming nomination will be more contentious than that of John Roberts (search) for chief justice.

"I have raised a certain cautionary signal," Specter told reporters outside the Executive Mansion on Wednesday, "but I believe the next nomination is going to be a great deal more contentious than the Roberts' nomination. I say that because, bubbling just below the surface was a lot of frustration in the hearing that we just concluded."

Many Democrats last week blasted Roberts during 17 hours of confirmation hearings for not answering their questions more fully. Roberts argued that he was just following the precedent set by previous Supreme Court nominees, who refused to answer questions that may commit them to one position or another on controversial topics that could come before the court.

During those hearings, Republicans repeatedly reminded Democrats that this approach was not just allowed but encouraged during the confirmation hearings for Ruth Bader Ginsburg (search).

Specter also said Wednesday that he suggested that the president delay picking O'Connor's replacement until more is known about Roberts, who is likely to be confirmed soon as the successor to the late William H. Rehnquist (search). A Judiciary Committee vote on Roberts is scheduled for Thursday, which means the full Senate likely will vote on the nomination next week.

Specter said he had spoken to O'Connor and she is prepared to stay on until June 2006 if asked. "It would be quite a sacrifice for her, but she's prepared to do it if she is asked. By next June we'll know a lot more about Judge Roberts ... than we do today," Specter said.

But Bush didn't seem to embrace the idea of a long cooling off period.

"The president was noncommittal," Specter said. "The body language was not very positive."

Leading senators floated the names of about a dozen candidates to fill O'Connor's vacancy on the high court, but Bush kept his list to himself during the meeting.

The senators did not identify the prospective justices they suggested to the president. Among candidates widely mentioned are: federal appellate judges Priscilla Richman Owen, Edith Brown Clement, Edith Holland Jones, Emilio Garza, Edward Charles Prado, Alice Batchelder, Karen Williams, Janice Rogers Brown, J. Michael Luttig, J. Harvie Wilkinson, Michael McConnell and Samuel Alito.

Reid said Tuesday he would view it as a "poke in the eye with a sharp stick" if Bush nominated any of the 10 appeals court nominees whom Democrats blocked in recent years, including some who were later confirmed. That group includes federal appellate judges Owen and Brown.

The meeting was similar to one that Bush held in July, one week before he nominated Roberts to fill O'Connor's shoes. Bush later offered Roberts for the higher job — to be chief justice of the United States.

Senate Majority Leader Bill Frist, R-Miss., said the session marked the formal beginning of consultations between the White House and Capitol Hill on the additional vacant seat, although Bush advisers previously held informal discussions with senators on the second nomination.

The 40-minute session Wednesday was also attended by Vice President Dick Cheney and White House chief of staff Andy Card.

Frist said he advised the president not to embrace Specter's idea for him to delay the second nomination. He said if Bush's second nomination came within the next 10 days, the Senate would be able to handle that nomination in a timely fashion. "I believe we can do it by Thanksgiving, if that nomination comes quickly enough," Frist said.

Senate Democratic Leader Harry Reid joked, "it's a cinch by Christmas."

Reid, who said Tuesday he will oppose Roberts' confirmation, said Bush seemed open to the senators' suggestions, but said the discussion was one-way. He said, however, that he thought it was a "tremendously good start," and said Democrats have had numerous opportunities to meet with White House counsel Harriet Miers' on the issue.

"There was a discussion of names," the Nevada Democrat said. "It was mainly our suggesting names to him and talking about names to him. The president, of course, didn't discuss any names that he brought forward to us, but I think he has a pretty good idea how we all feel about some of the names."

When one reporter asked if the senators brought up any names that would be unacceptable, Reid said "yes" and turned and walked away.

White House press secretary Scott McClellan described the meeting as "cordial" and said the president was considering a diverse list of prospective nominees. Asked whether the president agrees with Specter that the next nomination would be more "contentious," McClellan said the White House hopes the Senate will move forward in a "civil and dignified way."

Naming the first Hispanic to the court would make history and boost GOP efforts to woo the fast-growing voting bloc.

The list of Hispanic candidates includes: Attorney General Alberto Gonzales, federal appellate judges Emilio Garza and Edward Charles Prado, along with Miguel Estrada, a conservative young lawyer whose nomination to the U.S. Court of Appeals for the District of Columbia Circuit was thwarted by Senate Democrats.

Other candidates include Larry Thompson, the federal government's highest ranking black law enforcement official when he was deputy attorney general during Bush's first term, and Maura Corrigan, a member of the Michigan Supreme Court.

The ranking Democrat on the Judiciary Committee, Sen. Patrick Leahy (search), urged the president to consider non-judges and refrain from nominating someone who would be a "lightning rod" — a justice who would represent just one segment of society, or one segment of the Republican Party. If he did, that could deadlock the Senate and possibly even result in a filibuster, Leahy warned.

"We all recognize the fact that Judge Roberts will be confirmed as chief justice," said the senator from Vermont. "But the next one is the one everybody worries about and again I urge, as I have before, I urge the president to be a uniter not a divider."

The Supreme Court doesn't exist for either political party, but for all 280 million Americans, Leahy said, adding that Bush might want to fill the second vacancy with someone who is not already a judge, someone outside the "judicial monastery."

"You should be able to look that court and say 'I'm going to get a fair shake.' I may win. I may lose, but it's going to be based on my case and not who I am or what my political leanings might be," he said.

Specter said he was concerned about the balance of power between Congress and the court. He said that O'Connor to stay on the court for awhile would give the nation a chance to better understand Roberts' judicial philosophy.

"There is a possibility of a third vacancy with Justice [John Paul] Stevens, that has been rumored," Specter said. "He is 85, but in good health. But if that comes in the next year — with three new justices — a shift in the court. And that's a problem for both the right and the left."

The Associated Press contributed to this report.