CNN and Fox News are reporting that Bush's pick is Harriot Miers. RedState.org confirms.
Miers is one of the names I've seen floated about as a "moderate" choice for Bush, although I haven't heard on what this is based.
If this pick does upset the far right, expect Bush's numbers to finally crack down below the 35% baseline, as I doubt any pick of his will do much to win back independents and liberals at this point.
Update [2005-10-3 7:41:46 by WAmod]: Darksyde and a few others rightly point out that this could be another Bush head fake. Meanwhile, the right
flips out
Update [2005-10-3 8:6:48 by WAmod]: The press conference has started and it's definetly Miers, unless Bush is planning some kind of David Blane style magic trick on stage.