T.J.'s post pretty much explains it, but it might help you to know also that there is a maximum amount of fat per day that you can take out of your fat cells, so there is a limit on how many calories you can get per day from internal sources. And this limit goes down, of course, as you burn off your excess fat.
Richard did a fascinating post on this in the Science forum, and it explains why, in general, we need to eat, even when we are getting calories from our excess fat, and why lean people have trouble fasting (of course, the body can also use muscle tissue for fuel, but that is usually not a good thing).