It seems like a silly question, as we tend to think of spaghetti and meatballs as an Italian feast. But like many Chinese-American recipes, what we eat in the U.S. is quite different from what you'll find in the old country.
If you go to Italy, you will not find a dish called spaghetti and meatballs. And if you do, it is probably to satisfy the palate of the American tourist. So if not Italy, where does this dish come from? Meatballs in general have multiple creation stories all across the world from köttbullars in Sweden to the various köftes in Turkey. Yes, Italy has its version of meatballs called polpettes, but they differ from their American counterpart in multiple ways. They are primarily eaten as a meal itself (plain) or in soups and made with any meat from turkey to fish. Often, they are no bigger in size than golf balls; in the region of Abruzzo, they can be no bigger in size than marbles and called polpettines.
So there are meatballs in Italy. And marinara sauce. And spaghetti noodles. But combining them was a process made in America. Read about how Italians immigrants in the U.S. developed the spaghetti and meatballs we grew up on. Link
(Image credit: Flickr user Roger Ferrer Ibáñez)