IIRC, Sorkin didn't want to reference any presidents after JFK, but Josh mentioned LBJ at one point (though that could have been after Sorkin left, I forget). And the S2 premiere has a Reagan-named building sign clearly visible in the distance, but that was non-intentional. Sorkin also tried not to reference what year it was, but then wrote a discussion about whether 2000 or 2001 is the turn of the millennium.
The more important question is when in their AU major campaign finance reform was enacted, because those characters sure as hell don't live in our
big money-infested scene.