Hillary doesn't need a Karl Rove. She knows that a lot of conservatives are mad at Bush on some issues that she doesn't mind agreeing with them on. I think we're going to see a lot of this sort of thing in her preparations for a potential White House run. Many conservatives think Bush is weak on immigration (I happen to agree with Bush's main driving force here, so I'm not one of them).
If she could pick up the many voters who didn't vote in this election (or voted for Peroutka or Badnarik) because they thought Bush was too liberal on some of their key issues, then she may be able to beat even Rudy Giuliani, who of course is going to be fairly unattractive to all the arch-conservatives who don't recognize the pragmatic reasons to vote for the better candidate among the ones with a chance of winning.
On the other hand, these same voters that she's hoping to attract include a large contingent who would never vote for anyone who uses the euphemism 'choice' to describe abortion, and she does it as often as possible. They also tend to be the kind of people who don't like the obstructionism she's heavy-handedly supported with judge appointments. Even the more libertarian part of this group, largely concentrated in northern New England and western states. This won't help her get any sourthern states, but it might help her keep Washington and Oregon, which have moved more to the right in this election, and it might help her gain New Mexico, Arizona, Colorado, and Nevada. Of course, Giuliani, who I think it the most likely to get the Republican nomination if he wants it, is sort of the king of Homeland Security merely for being in the right place at the right time and doing what turned out to be a fine job. So maybe this won't help her much except to keep swing voters on the terrorism issue from automatically seeing Giuliani as the obvious choice.
All of this is so utterly speculative that it's worth very little, because so many things could happen between now and then, and so many others could step into the ring and present a better case to their parties for getting the nomination (and we have no clear sign from either Hillary or Rudy that they will run at all). Yet these are the kinds of issues anyone even considering a run for the presidency in 2008 needs to be thinking about now to avoid the situation John Kerry found himself, where on some issues he just didn't know whether to say one thing or another out of not knowing who needed to be pleased the most and on other issues he just didn't have a clear view that could easily remain constant. I know he denies both charges, and in many cases the charges don't hold up, but I think most pundits are recognizing that these things were true of at lease some of what he did, and I think they're right.