White House officials say President Bush will announce his new Supreme Court nominee within the next few days.
Mr. Bush was forced to pick a new candidate for the court after his previous choice, White House counsel Harriet Miers, withdrew her nomination on Thursday.
The president is said to have a pool of candidates that includes several federal appeals court judges, a Republican senator and a prominent Washington lawyer.
Mr. Bush has said he will choose a new nominee in "a timely manner," but Democratic Senator Charles Schumer, who sits on the Judiciary Committee, is urging the president to take time and consult with the Senate.
There had been mounting criticism of Harriet Miers, especially among members of the president's own Republican party. Some critics faulted Ms. Miers for a lack of judicial experience, and others asked if her judicial philosophy was conservative enough.
Retiring Justice Sandra Day O'Connor will remain on the court until the Senate confirms her successor.