i just used the spread sheet listed above (thanks for the link) and came up with $16K for a 20K mile/6 month trip. I went high on the lodging numbers so that should cover emergencies I think. Out west camping can be very inexpensive or free, on the east coast, not so much and finding free camping in the east is harder. 20K miles over 6 months works out to 111 miles a day which is a nice pace for an extended trip I think. On 2-3 week vacation trips I usually average 350 miles a day and feel rushed the whole way.
With your budget you're gonna have to earn money along the way. $3600 will get you started but won't last long. Go for it and just figure it out along the way. Good luck.
― Tom Waits
Don't you know there ain't no devil, it's just God when he's drunk.