Senate Judiciary Committee Chairman Arlen Specter (R-Pa.) complicated the already dizzying calculus about the future of the Supreme Court by speculating at length yesterday about the possibility that Justice Sandra Day O'Connor would stay if President Bush elevated her to chief justice.

Most Republican officials interviewed this weekend said they expect Chief Justice William H. Rehnquist to announce his resignation soon, although they said they had no hard evidence of that. Specter said on CBS's "Face the Nation" that his "own analysis is that the chief does not intend to step down as long as his health holds up." But then he all but endorsed the idea that O'Connor, whose swing vote has both vexed and pleased conservatives, would be a shrewd choice for chief.

"I think it would be very tempting if the president said to Justice O'Connor, 'You could help the country now,' " Specter said. "She has received so much adulation that a confirmation proceeding would be more like a coronation, and she might be willing to stay on for a year or so." The chairman said he had heard "senators who had made that suggestion to Justice O'Connor, and that the response that I heard was that she said she was flattered -- that she didn't say no."

Specter, cognizant of conservatives' wariness of his moderate views, added: "I don't want to jinx it. If I say it's a good idea, there's going to be an upsurge across the country against it."

A separate confirmation hearing would be necessary if one of the current justices were elevated to chief. O'Connor said in her resignation letter July 1 that she would retire upon the confirmation of her successor. Rehnquist's departure would mean at least two confirmation hearings, perhaps helping Bush by allowing him to balance his picks to please more than one constituency.

Bush is scheduled to meet with senators from both parties tomorrow, but Republican officials said they do not expect him to choose a nominee until the last week of July.

Republican aides said White House Chief of Staff Andrew H. Card Jr., Deputy Chief of Staff Karl Rove and counsel Harriet Miers are leading what the White House plans to call an unprecedented effort at outreach.

"Dozens of senators are getting phone calls from top White House staff," said a Republican aide involved in the process who spoke on the condition of anonymity. "They are being asked to offer their opinion about the qualities a nominee should have in terms of judicial temperament, and they are asking them to offer suggestions of names."

Sen. Charles E. Schumer (D-N.Y.) was reported last week to have said that his party was considering going to war over the court pick. But he said on NBC's "Meet the Press" that he sees hopeful signs Bush will come up with a "consensus nominee."

"What I said was that we will not roll over if they choose an extreme nominee," Schumer said, calling for "active and real consultation." Schumer is chairman of the Democratic Senatorial Campaign Committee and has sent e-mails calling on supporters to "keep the pressure on" to make sure the Bush meeting with senators "is more than just a courtesy call."

At noon Friday, Senate Majority Leader Bill Frist (R-Tenn.) -- who was visiting the Great Rift Valley in Tanzania -- held a half-hour conference call for Republican senators. Participants recalled that Frist said the party's message would call for a fair and dignified process, good committee work, an up-or-down vote on the nominee, and a confirmed nominee by the time the Supreme Court returns on Oct. 3. Frist has also been e-mailing extensively with senators while he has been away, aides said.

Sen. Charles E. Schumer (D-N.Y.) says Democrats will fight "an extreme nominee." Senate GOP leader Bill Frist has stressed process issues.