I know that the sentiment on this board is that you will do fine sleeping two nights in coach, but with a bad back and being a large person, I would urge you to think twice about it.
First: Amtrak long distance coach seats are not comparable to airline first class seats. There is no comparison to international long-haul sleeper seats, but even compared to domestic first, Amtrak coach is not an equal. The Amtrak seat pitch (leg room) may be as much or more than domestic first, but the Amtrak seats are much narrower and the seat design, comfort and cushioning is much more like airline coach. The recline angle is somewhat greater than airline coach but still you are upright to the degree that you will have to curl up or lean against the window to sleep. It is not a natural sleeping position: at least not for me (and at 5'5", 130 pounds, no one has ever confused me with a linebacker). Sleeping in coach on Amtrak is a very back unfriendly situation, and you will have to sleep that way for two consecutive nights.
I would urge you to look into a roomette. With the right timing you can get a decent fare and the free meals help offset the fare differential. The benefit is a real bed which will keep your back issues under control and will let you enjoy the train ride pain free.
