How would you define thoroughly ?
See all 48 continental states? Actually there are 49 continental states (only Hawaii is offshore). It is possible to drive through all 49 continental in about four months. But to thoroughly see even 1/4 of them would take a lifetime. I have driven around 47 of the 50 US states, logged several hundred thousand miles and figure I have seen about 30% of the country.
I can easily spend $10,000 in a month on the road, however, if you are frugal, drive a vehicle that only consumes fuel and oil (no repairs), rarely, if ever, eat expensive food, I would think you could stretch your road trip adventure to six months.
A number of roadtrippers have completed tours of the lower 48 states. Check out our Journals/Travelogs page at http://www.roadtripamerica.com/links/travelogs.htm and especially look at the adventures of "Destination Unknown", "Quest 4" and "The 100 day Road Trip to 50 States" found on the http://www.roadtripamerica.com/links/routes.htm page.
Go have an adventure!