Combine tomato sauce, tomato paste, water, onion, garlic, mushrooms with liquid, nutmeg, and sugar in a oven. Bring to a boil on top of the stove. Meanwhile, preheat the oven to 250°F.
Cover and cook sauce in the oven for 2 hours. (Sauce can be cooked on top of the stove if simmered very slowly). After 2 hours, add ground beef. (You can crumble it into the sauce or shape it into meatballs about 1 inch in diameter.) Cook 1 hour.
Add tomato juice or water and cheese and cook for 20 minutes. While sauce is cooking, prepare spaghetti al dente, following directions on package. (Be careful not to overcook spaghetti. Overcooked spaghetti will probably be too soft and will stick together.) Drain spaghetti and place on a deep platter. Cover with sauce and serve.