Actually, speculation about Bush’s next nomination to the Supreme Court began within hours of the announcement of Chief Justice Rehnquist’s death, and I confess to having been one of the culprits. My thought was that Bush would lean towards someone he appointed judge because that person would have less of a record to shoot at. Todd Zywicki at the Volokh Conspiracy agrees that prior Bush nominees have the advantage, but cites a different (and I think more persuasive) reason. He points out that Bush has great faith in his ability to judge people and likes to “promote from within” the circle of people who have impressed him enough to receive a past appointment.
Thus, Zywicki reasons:
If I am correct in this assessment of the President’s decision-making style, this would suggest that his next nomination would likely be from the crop of judges that he has appointed since becoming President. This would include Brown, Clement, or McConnell, but not more experienced luminaries such as Luttig, Jones, or Wilkinson.
If Bush is leaning towards appointing a female, Brown and Clement have an advantage. But Orin Kerr, also at Volokh, finds it unlikely that Bush will nominate Brown because her “hard core libertarian views” make it unlikely that she will vote conservative in a consistent way.
President Bush has appointed Alberto Gonzales repeatedly, although not to a federal judgeship. However, Erick at Confirm Them has been told by a source “close to the White House” that Gonzales has taken his name out of consideration. I tend to discount this sort of talk, though.
UPDATE: Professor Bainbridge has posted his odds for those he views as the four leading contenders. They are: