WASHINGTON (CNN) -- President Bush nominated White House counsel Harriet Miers on Monday to replace retiring Supreme Court Justice Sandra Day O'Connor.

Miers, 60, was the first woman to head the State Bar of Texas. She has never been a judge.

An outspoken supporter of the Bush administration, she was a leader of its search for potential candidates to fill Supreme Court posts. A White House official said that at the same time, Bush considered her as a nominee without her knowledge.

In a televised announcement from the White House, Bush called Miers exceptionally well-suited for the high court. Miers has devoted her life to the rule of law and the cause of justice, he said.

He called on the Senate to review her qualifications thoroughly and fairly and to vote on her nomination promptly.

It is the responsibility of every generation to be true to the founders' vision of the proper role of the courts in our society, she said.

If the Senate confirms Miers, she would join Ruth Bader Ginsburg as the second sitting female justice on the bench. O'Connor became the court's first female justice in 1981.

Bush offered her the job Sunday night over dinner in the White House residence, White House sources said.

During the summer, a vetting process for Miers took place once the president began considering her.

Bush took seriously suggestions by Senate Judiciary Committee Chairman Arlen Specter, R-Pennsylvania, and ranking Sen. Patrick Leahy, D-Vermont, that the president consider candidates from outside the appellate courts, the sources said.

More recently, Miers helped lead the administration's search for potential candidates to fill Supreme Court posts.

At the same time, a White House official said that Bush considered her as a nominee without her knowledge.

Harriet Miers is an intelligent lawyer who shares the president's judicial philosophy, said Leonard Leo of the conservative Federalist Society.

She has demonstrated that in her capacity as White House counsel and a senior administration official as well as an active member of the organized bar.

Quietly, some conservatives involved in the White House's nominee selection consultation process said they are concerned with Bush's pick.

The reaction of many conservatives today will be that the president has made possibly the most unqualified choice since Abe Fortas who had been the president's lawyer, said conservative activist Manuel Miranda of the Third Branch Conference, referring to President Lyndon B. Johnson's pick to the high court in 1965.

The nomination of a nominee with no judicial record is a significant failure for the advisers that the White House gathered around it. However, the president deserves the benefit of a doubt, the nominee deserves the benefit of hearings, and every nominee deserves an up-or-down vote.

The Concerned Women for America, another conservative group, also took a wait-and-see approach on Miers.

We give Harriet Miers the benefit of the doubt because thus far, President Bush has selected nominees to the federal courts who are committed to the written Constitution, said Jan LaRue, chief counsel of the group. Whether we can support her will depend on what we learn from her record and the hearing process.

One Republican official said that many had expectations that Bush's pick would be a known conservative, adding that he was surprised by the president's choice.

Republicans were hoping for a clear conservative, the official said. It's going to be heavy lifting for us and the White House.

Another conservative source who was involved in the selection consultation process said Miers was not a big surprise and that she had always been someone under serious consideration.

She's a good conservative, the source said. She does share the president's views about law and public policy. But she is not well-known, which is going to be part of the challenge.

Schumer continued, There's hope that Harriet Miers is a mainstream nominee. ... Given the fact that the extreme wing of the president's party was demanding someone of fealty to their views, this is a good first day in the process that begins to fill the seat of Sandra Day O'Connor.

Senate Minority Leader Harry Reid, D-Nevada, was complimentary of Miers.

I like Harriet Miers, Reid said in a statement. As White House counsel, she has worked with me in a courteous and professional manner. I am also impressed with the fact that she was a trailblazer for women as managing partner of a major Dallas law firm and as the first woman president of the Texas Bar Association.

The announcement came shortly before justices were to begin a new term with new Supreme Court Chief Justice John Roberts, who is the youngest member of the high court.

This is a situation where, from the very moment the justices start back up in October, they're going to be very divided, said Lazarus, who authored Closed Chambers, a book on the justices. It's going to be a lot of friction inside the building.

O'Connor announced her retirement in July. Bush initially chose Roberts for her seat, but the September 3 death of Chief Justice William Rehnquist changed the White House's strategy.

O'Connor has said she will stay on until she is replaced, making her role in the upcoming term unclear. Under court rules, a justice's vote does not count until a ruling is issued, a process that can take weeks or months.

Many legal scholars question whether O'Connor would want to continue hearing cases if her replacement takes over before rulings are issued, thereby negating her vote.