Not all liberals, and it depends on how you define it.
When I think "elitist" I tend to picture somebody who believes themselves inherently superior, often in the face of conflicting objective evidence. In the same vein, the term "egghead" the way I would use it is somebody who THINKS they're smarter than everyone else.
I've noticed that a lot of truly superior people are often humble about it.
Not all liberals by any means are elitist, or possessed of a large sense of their own superiority. Heck, not even all Democratic presidents by a long shot.
A list of the top of my head of recent Democratic presidents I don't think were elitists would include Johnson, Carter, and Clinton.
Hmmmm. I just realized that Democratic candidates are often elitist (Gore, Kerry, Obama) but the winners aren't.