Bush will follow form and tic tac toe to the far right on replacing O'Connor. I would say tack in the nautical sense, but Bush likes to keep things simple and leave the complex game-playing to Rove and the rest of the boys. So tic tac toe it is.
CHRISTMAS FOR THE FAR RIGHT--the Bush administration has wanted to move the Federal Judiciary to the far right as much as possible (that's the reason for hanging in on Owens, Brown, etc.). The idea is to the right-wing is to lock in the courts while they have control over the Presidency and Congress. That way, their judicial legacy will carry on even if the Republicans start losing elections. The stakes are especially high in O'Connor's replacement because she was such a swing vote. Bush is going to appoint the hardest right-winger he can. Maybe Janice Brown of the "New Deal was Socialism" fame has a sister somewhere.
A GRATUITOUS SIDE PREDICTION--there will be a steady dribble of articles in the mainstream media about how "surprisingly moderate" the nominee is. After all, Caligula was moderate compared to Nero.
RED MEAT FOR DOWN DOGS-- from Bush's (really Rove's) point of view, tacking right would also be good politics because it would mobilize the GOP's right-wing popular base and provide tons of grist for the talk-radio, Fox, and right-wing religious mill. The right-wing has been down at the mouth about the Iraq war lately and there's been a softening on some issues in Bush's poll numbers among Republicans. The Bush administration will view tacking right on O'Connor's appointment as a way to prop up their standing with their base heading into the 2006 elections. The mainstream media keeps thinking that Bush will start trying to appeal to moderates, but the strategy will be for a right-wing media blitz to intimidate easy-to-frighten moderate voters into agreeing with Bush.
ANOTHER GRATUITOUS SIDE PREDICTION--There will be no coverage from the Mainstream media on how Bush's appointment plays into the politics of the extreme Republican right. Partly because of their fear of the right, the mainstream media is still into the idea of translating the right into a moderate/liberal political language. The media never really catches up to the right.
WHEN IN DOUBT, CONFRONT--Bush (ok, probably Rove) has figured out that confronting Congressional Democrats is good for business. First, he's won almost all the big smackdowns (the 2001 tax bill, authorization to invade, appointments of Owens and Brown, the Homeland Security Bill, etc.). But more to the point, Bush has discovered that the public generally sympathizes with the President in situations of intense conflict with the opposition in Congress. This can be seen during the government shutdown battle between Clinton and Gingrich. It wasn't so much that Gingrich was stupid and arrogant (although he was) but that Clinton had the advantage of being President. Bush can be stupid and arrogant (let me count the ways), but can get away with it because he's president. As a result, the Bush administration already has the Democrats in a box. If the Dems don't fight a far right-wing appointment, then their own base could get discouraged, stop contributing to the party, and start looking for a party with more backbone (always a temptation). If the Dems do fight hard, the public will blame them rather than Bush for the ugliness of the confrontation.
Nominating a hard-line right-winger looks like a winner for Bush. Of course, he could choose to reward his favorite torture lawyer as well.