WASHINGTON – Senator Schumer, of New York, said yesterday that Democrats “will not roll over” for an extreme nominee for the Supreme Court, and White House officials went forward with the process of consulting what they said will eventually be dozens of senators from both parties about whom President Bush should pick.

Both parties used the weekend as a reprieve to hone their messages ahead of what they believe could be a statement today from Chief Justice Rehnquist that he will retire. Top officials said they had no hard evidence Chief Justice Rehnquist plans such an announcement, and a key Republican senator even said he doubts it is true.

Chief Justice Rehnquist’s departure would mean at least two confirmation hearings, complicating the job for the Senate but perhaps helping Mr. Bush by allowing him to balance his picks to please more than one constituency.

Mr. 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 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 refused to be named. “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.”

The judiciary committee chairman, Arlen Specter, a Republican of Pennsylvania, said he believes Chief Justice Rehnquist is going to stay as long as he can. “There is a certain mystique and inscrutability about the chief, but my own analysis is that the chief does not intend to step down as long as his health holds up,” Mr. Specter said on CBS’s “Face the Nation.” [Senator Specter also suggested, however, that Mr. Bush could nominate Justice O’Connor to the position of chief justice if it opens up, even though she is retiring, according to the New York Times Web site.]

Mr. Schumer was reported last week to have said on an Amtrak train that his party was considering going to war over the court pick, but he said yesterday on “Meet the Press” that he sees hopeful signs that Mr. Bush will come up with a “consensus nominee.”

“What I said was that we will not roll over if they choose an extreme nominee,” Mr. Schumer said, calling for “active and real consultation.” He issued a news release contending that it is “perfectly okay to ask judicial nominees about constitutional issues and their views on decided cases.” White House officials and key Republican senators have been making the opposite case, contending that specific personal views should be off limits.