A contrary view
As a rebuttal to my own post below, there is one possible alternate reading to the nomination of Meiers. The pattern in Bush's second term has been to nominate close associates to positions of power (Condi to State, Gonzales to Justice, etc.) Meiers could just be the next iteration of that pattern. Andrew Sullivan makes the point:
Think of her as a very capable indentured servant of the Bush family. She'll do what they want. She'll be a very, very tough nut to crack in the hearings. And I have no idea about her judicial philosophy. But I imagine that's the point. When I described her as a flunky last July, a source close to Bush told me: "Don't mess with Harriet." I think they've found someone whose personal loyalty to Bush exceeds even Gonzales'. And in some ways, I see this very personal, very crony appointment to be a response to being told he couldn't pick his main man, Alberto. Harriet is his main woman. I reserve judgment on her fitness to serve on the court.
Bush may not have made a political calculation at all in making this appointment. He may have just decided that he wanted a sycophant on the court and if, as Andrew suggests, he couldn't get Gonzalez, at least he would get Meiers.
Bush likes to get his way. As much as Bush has a history of screwing over enemies, he also has a history of screwing over friends. It is possible that the pushback he received from the wingers on the idea of nominating Gonzalez just pissed him off enough that he decided to stick it to them with Meiers.
Just another example of his legendary petulence?