Shopping only at a Wal-Mart isn't so bad, I do it all the time.
Bread is most likely going to be a problem; I have never found a vegan loaf there. You may have more luck with tortillas, but you will probably only find them around the bakery/deli section (look for a brand called Joseph's), and watch out for L-cysteine.
Other than that though, eating vegan at Wal-Mart is fairly easy. Beans (they even have vegetarian baked beans), rice (several of the pre-packaged rices are vegan, usually under a brand called Near East), grains, fruits, veggies, soy milk, tofu, energy bars like Luna and Odwalla, etc. If you want cereal, all of Kashi's organic line is vegan (and one of their frozen dinners is too). Wal-Mart also carries vegan condiments like Annie's teriyaki sauce that are actually marked vegetarian and other foods like hummus. For the rest, though, you will just have to read the ingredients.
Keep the foods simple, and you shouldn't have a problem. This website is helpful to me: http://www.happycow.net/health-animal-ingredients.html