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President Bush offered no insight and gave no comment about his next nominee for the U.S. Supreme Court as he entered the White House Sunday.

Nonetheless, his expected afternoon return from Camp David renewed anxious expectations in Washington, D.C., that a new high court nominee could be named at any time.

"I think Monday, and I think the first name will be Michael," syndicated columnist Charles Krauthammer said Sunday, guessing when the nominee to replace retiring Justice Sandra Day O'Connor would be named and who it may possibly be.

Krauthammer said he is rooting for appeals court judges Michael McConnell (search) or possibly Michael Luttig (search), both champions of conservatives and respected by liberal legal scholars. He also likes Circuit Court Judge Sam Alito (search).

"If you pick a nominee with the stature of (Supreme Court Chief Justice) John Roberts, and there are several judges out there who have been on the courts for a dozen years or so, a Michael McConnell, a Michael Luttig, Sam Alito, these are three judges who have been there for years, who have sterling records endorsed by law professors," Krauthammer told FOX News.

McConnell is a judge for the 10th Circuit Court of Appeals in Denver, Colo. He was nominated by President Bush in 2001 and confirmed by the Senate in 2002. He clerked for Justice William Brennan and worked as associate general counsel at the Office of Management and Budget early in the Reagan administration. He was a law professor for 17 years before being joining the appeals court.

Luttig now serves on the 4th Circuit Court of Appeals in Virginia. He clerked for Supreme Court Justice Antonin Scalia when Scalia served on the federal appeals court and for Chief Justice Warren Burger at the Supreme Court. He worked in the Justice Department during the presidency of George H.W. Bush and the White House counsel's office during the Reagan administration.

Krauthammer said both nominees have impeccable credentials and that while conservative, they would be difficult to oppose, particularly by the seven moderate Democrats who earlier this year helped establish the "Gang of 14" with seven Republican counterparts to prevent Democratic filibusters of some of the president's federal appeals nominees.

"I can't imagine that the seven Democrats there would endorse blocking and preventing a vote on a man like a Michael McConnell, who was endorsed, I think unanimously, on the circuit court, who got a letter of endorsement from liberal law professors because of his stature as a thinker, it's going to be hard to" reject him, he said.

Alito was nominated by the first President Bush to serve on the 3rd Circuit Court of Appeals in Philadelphia. A former deputy assistant to Attorney General Ed Meese in the mid-1980s, he also worked in President Reagan's solicitor general office.

He is known for being quiet, reserved and well-versed in constitutional law, and has a record that should please many conservatives. However, that record could also work against him.

Newsweek columnist Eleanor Clift said Alito's role as the sole dissenter on the 3rd Circuit court in the 1992 Planned Parenthood v. Casey decision, which struck down a Pennsylvania law that required women to inform their husbands before they got an abortion, could cause Democratic objections. The circuit court's decision was upheld by the U.S. Supreme Court.

"That (case) certainly would come up. I think we know the least about him. There is a fight no matter what. It depends on how big a fight the White House wants and how big a fight the Democrats dare weigh depending on the credentials of the nominee," Clift told FOX News.

Whoever the choice, most Washington insiders agree that the president is unlikely to disappoint his conservative base, which put up such a fight over the president's last nominee, Harriet Miers, that last week she withdrew her name from consideration. Miers asked to be excused after lawmakers demanded her records while White House counsel, saying that was the only paper trail on constitutional law that she had.

Conservatives cheered at the decision, even if they perceived her reasoning to be a pretext. They said Miers was given a graceful out because she was not qualified to sit on the nation's highest court.

"We were not happy (with the Miers nomination), and there was concern among senators in the Senate, Republicans and some Democrats, about the qualifications of this nominee. I'm sure she's a fine lady and a good lawyer in many respects. But there was concern about, you know, the qualifications for the Supreme Court, so it was putting a cloud over things," Sen. Trent Lott R-Miss., told "FOX News Sunday."

With only a few key Bush insiders likely in the know about the president's choice, Lott said he was confident the president's third choice for the seat would satisfy the right.

"I'm confident the president is going to pick a conservative, someone like John Roberts, and I am confident he will be confirmed," Lott said.

Sen. Chris Dodd, D-Conn., who appeared with Lott said Bush could pick a conservative in the vein of Roberts, but he needs to be careful not to cave in to the far right.

"Pick one that's not going to have to pass the litmus test of the extreme right in the country. If you do, I think the president gets terribly hurt by that," Dodd said.

Democratic strategist Bob Beckel added that he doesn't think conservatives can find another John Roberts.

"Alito or Luttig will guarantee a fight because neither one of those are like Roberts, they are way to the right of Roberts, both of them are borderline or out front against Roe v. Wade, which is not going to be acceptable to the Democratic Party. ... So if that's the ilk you're talking about, then I guarantee there's going to be a fight and maybe a fight is not so bad," Beckel said.

While other names are also being floated around, including former solicitor general Ted Olson and 5th Circuit Court judge Emilio Garza, Sen. John Cornyn, R-Texas., said his has not been one of them. A former Texas Supreme Court judge, Cornyn told ABC's "This Week" that he has not been contacted for the White House as a possible contender for the seat.

Cornyn said would like to see a woman replace O'Connor and he believes the nominee will most likely be a "judicial traditionalist" currently on the federal court.

Among the women named as possible contenders are 4th Circuit Court judge Karen Williams of South Carolina, 5th Circuit Court judges Priscilla Owen and Edith Hollan Jones and D.C. attorney Maureen Mahoney.

"[Mahoney] is a D.C. lawyer and she has been on a short list. She has a resume that mirrors John Roberts. She clerked for Rehnquist. She has argued a dozen cases before the Supreme Court. She's very well-qualified, highly thought of, and I think she got taken off the list because she argued on behalf of ... the University of Michigan in the affirmative action case. But it was a client and I don't know if the right is going to stand for any diversion," Clift said.

"I suspect he's going to produce a reliable conservative with a record that is transparent enough that the right will know where he or she stands," she added.

John Fund, an editorialist for The Wall Street Journal, said the nominee's beliefs and their records are two different matters. For instance, Mahoney argued against Title IX, which is supported by feminists.

"I think the people will distinguish between someone who argues on behalf of a client and someone who has personal views," he said.

"But the bottom line is if the decision comes in the next couple days, it has to be someone who has already been fully vetted and that narrows it down to about six people."