Mark Schmitt makes a great point:
If all they had to do was satisfy the hard right, they could probably do it, especially if they don't worry about the nominee being female or Hispanic. But there is another factor they have to deal with now: Arlen Specter. A year ago, Specter was humbled and compliant. Bush and Santorum had saved his Senate seat from a right-wing primary challenge, and Bush had protected him when there were right-wing objections to his taking the Judiciary Committee chairmanship. But now the politics are very different. What's the right going to do to him now? What's Bill Frist going to do to either protect him or hurt him? Nothing. What good is the protection of a humbled White House? And knowing a little bit about Specter, I'm guessing that he feels highly insulted by the fact of the Miers nomination and that he was expected to push it through. An angry, empowered Specter is not a pretty sight, and my guess will be that if they send up a hard-right movement conservative, especially on choice, Specter will no longer feel any obligation to do anything to move the nomination forward. It's going to be much harder to satisfy both the angry right and the angry moderate than it would have been a month ago to just nominate one of the plausible candidates.
In addition to a weakened White House, Frist has completely lost control and the Senate has devolved into fractious warfare between a variety of powerbases looking towards campaigns for the presidency. It is, for party discipline purposes, the absolute worst of all worlds. Plus, Specter just won another six year term, he's got Hodgkin's disease, the Christian-conservative senator in his state desperately needs his help campaigning, and the senators on his committee like him. He may not be invincible, but provoking a fight with the sick senator over his committee's independence isn't the sort of thing the GOP would be wise to pursue. After all, what's the next step? A tell-all book from an angry powerbroker decrying the religious right's outsized influence? No one wants that. And no one will risk creating it.
The politics, now, have really changed. We'll see if the Bush administration has noticed.