Lots of great tips in this thread. I tried to make a similar run last August from LA to Detroit after having made Detroit to LA in an old Cherokee, as I bought a Celica in San Francisco. I made it to LA, drove around LA for a two days, and the day before I was leaving LA to head home, this happened...
Of course, it happened after I spent a considerable amount of time/money/effort making sure it was capable of the trip back to Detroit. $4000 down the toilet for 5 glorious days of the car I'd wanted for so long.
So be careful, I wish you much luck.