Ed Kilgore says the religious right is tired of being teased:

I believe that Bush will send an extreme nominee to replace O'Connor, but I don't think it's specifically to appease the fundies -- it's to reignite the filibuster debate and get the rules changed before replacing Rehnquist. I don't buy Kilgore claim that the religious right will abandon the GOP if they're not happy with the pick, and the reason is that black voters still vote for Democrats at a rate of about 90%, even though the Democratic Party hasn't done much for black people in the last couple decades. While the black vote is not as organized a bloc as the religious conservative vote, and thus not as likely to up and quit the party all at once, I fail to see what the religious right will do. They won't vote Democrat, and they've been indoctrinated in the politicization of religion for a quarter century, so I don't see them just taking their votes and going home. A third party? It might work in some districts, but it wouldn't work nationally and it would definitely work their cause on balance.

Unfortunately, I doubt we'll ever know.