The national party organizations are strange beasts, enshrined in law with unique powers and constraints. It isn't entirely clear just what they're supposed to do. Obviously the DCCC and DSCC have more defined missions, but the DNC is kind of odd. During a presidential campaign or when there is a Democratic president it's basically an adjunct to the presidency or the candidate. In other times, their purpose is much less clear.
Now that Obama's the candidate, it will basically become his party. I don't know the extent to which that's inevitable or just custom, but presumably it will happen. We basically went from the Clinton party, to the McAuliffe years, and then the Dean years. And now...? I assume, perhaps incorrectly, that Dean will stay on at least in title until the election, though whether his authority will be eroded (by mutual agreement) is a question.
Anyway, not really insidery enough to know how all of this works. Maybe somebody who is should write a blog post about it!