I hitchhiked from GA to WA, and it only took me 3 weeks.. ( This was in 2009?? ) Years ago, I drove LA to Miami, only took me 8 nights? I stopped in New Orleans though, and visited with a buddy. So... If you are in Louisiana, "bayoubill," shouldn't take you more than 4 days!! Go to a truck stop, and see if somebody is heading west on the 10.. Once you hit NM, you want to head north.. It might even take you two days... Head to Denver, and grab a job in a Hydroponic Grow Store, or a Coffee Shop..
Good luck!!
Oh!! And keep your eyes open, hitchhiking is slightly dangerous, and often times illegal on/in certain towns, cities, streets, rodes, etc..