Believe it or not I've made boxcars out of thin white cardstock, thinner than the stuff business cards are made of. It's a little flimsy, but there are tricks that can help. Reinforce the corners with wood (basswood strips are cheap--get $2 worth and you can build several cars, especially if you model in a small scale. I model in O, and even then they last a while.) Fold over the edges and you'll get extra rigidity. Obviously, the more layers you have, the stiffer and stronger it will end up being, just like any other material. Finally, go to the hobby shop and buy a bottle of really thin CA glue. It'll probably cost you about $3 but will last a while. (Don't buy a tube of Krazy Glue at Wal-Mart; the hobby store stuff ends up being cheaper because it's a larger quantity.) Before you paint the body, apply a few drops of it here and there and let it soak. You'll be amazed how much it stiffens up. This is a trick model rocketers use to strengthen the bodies of their rockets. If it's good enough for them, I figure it ought to be good enough for us.
I prefer working in other materials, but I understand how cost can be a factor. If you're using thicker cardstock, especially stuff from food containers, it'll work even better. I say give it a shot. Even if you end up not being happy with the results, you'll learn a lot, and you'll be happier with the next project.
I'm not old enough to remember this (I'm 29) but I'm told that in the early days of HO model railroading, rolling stock made of paperboard was common, and railroad magazines would actually print car sides on thin cardboard and include them in the magazine. It was cheap, and there have been times in our history when it was the only thing available.