My guess is that the odds have just increased that Bush is planning to pick an unqualified extremist.
My evidence is the latest flurry in the papers concerning (1) the deliberately trumpeted "rift" between Bush and the radical right, emphasized by quoted statements from White House officials and from Senator Frist's office, and (2) Bush's statements today, quoted in the NY Times, emphasizing that he will not use any particular issue such as abortion as a litmus test, and that "I hope the United States Senate conducts themselves in a way that brings dignity to the process, and that the senators don't listen to the special interest groups, particularly those on the extremes."
From the standpoint of White House tactics, this strikes me as a head fake to the center, designed to position his choice as non-ideological and only the Democratic opposition as ideological. By picking an extremist, he avoids alienating the hard right, who are ostensibly being dissed in the above. If he planned to alienate them by picking a relative moderate, I would expect him to make noises at this stage about the importance of restoring constitutional principle or some such thing. (I.e., he would try to throw smoke in their eyes rather than in everyone else's eyes, on the view that his choice was politically safe enough not to need the pre-positioning.)
The alternative explanation is that the Schiavo affair et al have persuaded Bush/Rove that they genuinely need to steer clear of the hard right at all stages. But I still think that they are too obstinate, too wedded to the hard right and the energize-the-base strategy, and too fond of head fakes and deliberate misdirection for this alternative explanation to stand at this stage as the most likely one.