The Miers nomination has been such a huge blunder that one struggles to explain it. Probably, the explanations already out there are good enough (Card vs. Rove White House wars, Bush feeling adolescent defiance towards attacks on his cronyism, her lack of any paper trail, etc.). But here is an additional possibility that occurred to me. Its virtue is that it would suggest that Miers had a genuine advantage, from Bush's perspective, over any other possible appointee, thus making the risk (however ill-appreciated) of a hostile reception more worth taking.
Suppose the White House wanted a Justice who would not only vote its way on executive power issues (which is what Bush really seems to care about), but be a double agent, covertly consulting the White House during important cases regarding how to get 5 votes, what the other Justices were thinking, etc. Most prospective Bush appointees, even lockstep hard-line conservatives, probably would not dream of doing such a thing, and it would be dangerous even to ask them. [Maybe Gonzalez would do it, too, and Bush seems to have wanted to name him, but note that Gonzalez has a bit more prominence & career independence than Miers.]
Perhaps Bush knows that Miers is willing to play such a role.