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.
“A gentleman is someone who can play the accordion, but doesn't.”
― Tom Waits