Peggy Noonan has an interesting editorial today, where she speculates that some people in the Bush administration may be thinking about replacing Dick Cheney.
The main reason I can think of for Bush to do this is to be able to name his own successor. Here is where it gets tricky: If Bush names a potential presidential candidate, how many other potential candidates will get angry?
I expect Bush will not do anything like this until late 2007. That way any backlash will be limited to his last year in office.
As Peggy Noonan astutely points out, "The key thing is Iraq. George Bush cares deeply about Iraq and knows his legacy will be decided there.". Unfortunately, this does not limit the potential field much. I am not aware of any potential Republican candidates who would pull us out of Iraq.
But the Democrats would. So for Bush, the main consideration then has to be someone who can win. McCain and Guliani are electable, based on their appeal to moderate voters. But will they appeal to the conservative Republicans? If the Democrats nominate Hillary, I suspect the Republicans might be a little more flexible with their nomination. Republicans have a strong motivation towards "Anybody but Hillary".
One legacy factor Noonan fails to consider is Bush's Medicare fiasco. Bush would want that maintained, but McCain would undoubtedly gut it (he voted against it).
That leaves Guliani, although I admit I don't know where he stands on Bush's Medicare fiasco. If not Guliani, Bush might go for a dark horse candidate (George Allen?).
For the sake of proper disclosure, my personal favorite for 2008 at this point in time (I reserve the right to change my mind later) is Newt Gingrich, although I doubt he would get Bush's support.