To put it mildly, 2008 looks like it will be a struggle for the other side. Their options to improve the situation seem few, and they might be game for some unorthodox strategies that, even if extreme and inherently unlikely to succeed in normal conditions, just might be their best shot in what looks to be a very bad year if they passively let things develope in a conventional manner. Bush has a predilection for Hail Mary Passes anyway...
Two of their big structural advantages are slipping. Their loss in 2006 has already opened up something closer to parity in the money stream from the folks who have the money towards the Dems. Their vaunted advantage in the ground game is also clearly slipping in many states.
But their internal ideological divisions, while less predictable in their impact this far out, are likely to be even more of a problem for them. Simply put, their candidates who would seem most likely to do well in the general election, would seem to have the steepest path to nomination past the party's True Believers, who dominate the primary and caucus processes.
And this cycle, they do not have a candidate waiting in the wings who has been anointed by a process bypassing the primaries and caucuses. The President, of course, can't run again. Even his Vice-President this time around is not available.
Yet this President, while he himself cannot run, is even more motivated than usual to see his party hold on to the Executive branch. His potential legal problems, while perhaps not rising to the level that 1/3 of the GOP Senators could be persuaded to convict in an impeachment trial, and therefore not likely to lead to an impeachment attempt, are almost certainly enough to create the real risk of criminal prosecution should the Executive branch, and the appointment of US Attorneys, fall into Democratic hands in 2008. Yes, he could perhaps pardon himself as he leaves office, but that act, quite aside from a loss of pride if it has to be resorted to, is likely to lead to his Democratic successor having a much freer hand to honor extradition requests from other countries, whose citizens have been the chief victims of Bush's crimes. The President cannot pardon anyone on behalf of the legal regimes of other countries.
The President has in his hands one powerful means of maximizing the odds of a Republican victory in 2008. He could arrange to give the strongest possible candidate in the Republican stable the advantage of incumbency. This would probably help at least somewhat in the general, but the real importance would be to effectively shut down any intraparty conflict over the nomination, as the Party rallies to its already-in-office Commander-in-Chief. The half-way measure of having only Cheney resign, and replacing him with the favored candidate, might not be strong enough to foreclose serious competition for the nomination. Worse yet, it might hurt, and hurt seriously, in the general, because this is not exactly a very popular administration with the general electorate, and working for it as VP may not be a good character reference. For this thing to work, Bush would have to make the big leap, and have both Cheney resign, and then resign himself once the desired candidate is in place as Cheney's VP replacement.
This would work because it would meet the needs, at least immediate needs, of everyone whose assent is necessary to make it work. Bush gets an early out from a job he can't much enjoy anymore. Instead of going out as a failure because of his inability to admit error and accept responsibility, he goes out as someone who so accepted responsibility that he made the ultimate (political) sacrifice for the good of his party and country. The self-sacrifice, not incidentally, will make it so much easier for his successor to pardon him in the warm glow of the immediate aftermath, and poltically difficult for later administrations to allow his extradition. Many Repugs may not much like the moderate whom Bush will have to appoint to make this work, but they will be happy to hold their ideological noses to get rid of the pragmatic political albatross that BushCo has become for 2008, and replace it with the heroic narrative of a bold new Republican administration riding into town just in time to save America before the next election cycle (but not so far ahead that the honeymoon will wear off, and actual results be expected). Congressional Dems will, insofar as they see the practical political intent, not be very happy with these events, but will hardly be in a position to oppose a genuine moderate (I mean, as moderate as Republicans get) offered in a spirit of self-sacrifice by a President resigning for the good of the country, because he has finally admitted that Dem opponents of the war were right, both that the war was a mistake, and that it was so huge a mistake that there must be accountability. What would the Dems do, vote down this reasonable replacement, who, even if to the right of Attila the Hun, would have to be an improvement over Bush/Cheney? Would it be politically viable for them to insist that Bush appoint a Democrat to succeed himself? Less so than conviction for impeachment.
Of course this would have to be timed properly in order to work. They couldn't wait until a Republican who seems doomed to lose the general had already won the nomination fight, or this ploy would be so obvious a play to do over an unsuccessful nomination contest that the Dems would be able to insist that the Bush replacement be a true caretaker, someone who pledges not to accept the nomination at their convention. They also couldn't wait until the President was already in serious legal trouble, with impeachment underway, or even clearly looming, or the replacement President would be seen as the tool of a cynical ploy to rescue a criminal administration from its just legal desserts, and not the heroic savior who takes on the dirty job of cleaning up after a failed administration. The main reason that they would not do this is precisely because the President might not accept its necessity until events have progressed so far as to make it no longer a viable strategy.
Yes, none of this may come to pass, and which Repug would do best in the primaries is definitely a reasonable thing to be considering right now. But this scenario could happen, in which case the key consideration is which Repug, no matter his or her viability in a Repug intraparty conflict, would do best in the general in 2008. I think there's a reasonable chance that that's who we'll be up against, playing the role of redemptive hero/heroine with a whole ready-made narrative of Republican sin-repentance-redemption at his or her back. It could be the only way they'll win in 2008. And that is the single most powerful reason it would happen.