The lawyers and analysts, all of whom have been involved in directly or indirectly counseling the White House about Supreme Court selections, also said that because of Mr. Bush's desire to move quickly, he would probably choose from the roster of candidates whom he has considered before and whose backgrounds and records have been extensively researched.
The consensus among the handful of people who spoke about Mr. Bush's situation was that in addition to deciding whether he had the leeway to replace Justice O'Connor with a man, Mr. Bush will have to deal with other more pressing political questions in making his selection.
Among the questions: How much of his decision will be affected by a need to satisfy his conservative base, which shocked him with its widespread rejection of Ms. Miers?
And how much of a political fight with Democrats is he willing to risk by naming someone in the mold of the conservative Justices Antonin Scalia and Clarence Thomas. One decision about any new nominee that seems beyond doubt is that Mr. Bush and his aides - and they awkwardly still include Ms. Miers on this issue - will select a candidate with unassailable legal credentials and a firm grounding in constitutional law. Ms. Miers's experience as a corporate lawyer was dismissed as having little relevance, and her relative inexperience with constitutional issues and reasoning, the heart of the Supreme Court's work, was treated with disdain by Democrats and Republicans, liberals and conservatives.
One lawyer close to the president said that when Mr. Bush chose Ms. Miers he did so after concluding there was not a long roster of female candidates with whom he felt comfortable.
"When he chose her," said the lawyer, "she was one of three finalists and the other two were men."
The other two candidates, the lawyer said, were federal appeals court judges, Samuel A. Alito Jr. and J. Michael Luttig, both of whom remain leading candidates who would bring strong legal and judicial credentials to any confirmation battle.
Judge Luttig has been at the forefront of the campaign to press a new conservative judicial approach, first as a senior aide in the Reagan administration, where he helped select candidates for the bench, and now as a judge on the United States Court of Appeals for the Fourth Circuit, widely regarded as the boldest conservative appeals court in the nation.
Judge Alito, who was first named to the appeals court in Newark by President Bush's father, achieved acclaim for his stint in New Jersey as United States attorney, the state's chief federal prosecutor, during which he successfully prosecuted mobsters and white-collar criminals.
His jurisprudence, like that of Judge Luttig, has been solidly conservative and both are known for their strong and reasoned writing. But Judge Luttig and perhaps to a lesser extent, Judge Alito, would draw Democratic opposition.
A third male candidate is Judge J. Harvie Wilkinson III, also of the Fourth Circuit. He is considered someone who might be more palatable to moderate Democrats and someone the president might turn to if he is looking to avoid a major battle.
As for women, Mr. Bush could select Judge Priscilla R. Owen of Texas, whom he recently appointed to the United States Court of Appeals for the Fifth Circuit.
Judge Owen, whose record on the Texas Supreme Court established her as a strong opponent of legalized abortion, was confirmed to the federal bench in a compromise that ended a Democratic filibuster of her nomination. She would also probably provoke a major political battle if Mr. Bush tried to name her to the Supreme Court.
Two other possibilities are Judge Diane Sykes of the Seventh Circuit and Maureen Mahoney, who is not a judge, but someone whose profile resembles in many ways that of John G. Roberts Jr., the new chief justice. Like Chief Justice Roberts, Ms. Mahoney has a strong academic record - she is a graduate of the University of Chicago Law School - and has argued many cases before the Supreme Court both as a deputy solicitor general on behalf of the government and for private clients as well.
Some conservative lawyers said that Ms. Mahoney might be unacceptable to social conservatives because she successfully represented the University of Michigan in a 2003 Supreme Court case that preserved a measure of affirmative action in university admissions.
A former Wisconsin state judge and State Supreme Court justice, Judge Sykes has been active in the Federalist Society, an organization for conservatives trying to shift the courts rightward.
As for naming a Hispanic candidate, which many of associates of Mr. Bush say he would like to do, he is largely prevented from selecting his most likely choice in that category, Attorney General Alberto R. Gonzales.
In citing a reason for withdrawing Ms. Miers's nomination, Mr. Bush said he could not comply with the Senate Democrats' request for her work as his White House counsel because it would damage the ability of presidential advisers to give candid legal advice.
As Mr. Gonzales was Ms. Miers's predecessor as White House counsel, the same issue would arise.