You can either do it, or always wish you did. Your choice.
I have also seen much crazier things. A friend of mine from college who is a stand up comedian, decided to hitchhike his way from NYC to LA to "find Tom" of MySpace. He filmed his entire journey and shared it on the web. Additionally, he also crashed with all his MySpace friends the whole way so his cost is practically 0 (besides the bus tickets).
It's definitely doable on an even smaller budget :) Good luck and let me know when you arrive at the valley!
Just do it! I'd recommend doing the west coast bit if you leaning that way.
My way would be Chicago -> Seattle -> San Fran.If time and money and/or your desire permit then swing down the south for Austin -> New Orleans -> NY -> Boston.