The President that it best knows (at least until January 2009) is of course George W. Bush... and even with Bill Clinton it recognizes that the Republican-dominated Congress called the shots. Dubya was not the sort of President to serve as an introduction of American politics at the best. Earlier generations at least know Ronald Reagan.
I am of the infamous Gen X and I have thought that part of the reason for the Republican lean among Gen Xers was that we grew up observing Democratic failure (Carter) and Republican success (Reagan). Not that I agree with Reagan's philosophy, but he was successful in advancing his agenda.
However, those of us who are younger Gen Xers (born in the mid and late 70s) grew up under Bush I and Clinton. Those are the Presidents I mainly remember from my youth.
Given that today's generation grew up under Bush II, one of the worst Presidents in history, their Democratic lean is not surprising.