Breaking down fat costs a lot of oxygen. The body can run on fat if you have a lot of oxygen to spare. If the effort is causing you to breath heavily, then you are probably mostly burning faster carbohydrates (glycogen, a sort of sugary fuel the body has already stored in the muscles).

Running out of fast carbohydrates is (at least in biking) called "bonking". You'll feel extremely tired, maybe be shaking, and feeling dizzy. It's a blood sugar dip: a very low and long dip. Your brain usually runs on sugar too, so you'll feel stupid and angry. Your body still has fat stores, so your body can keep running - but at a much lower effort intensity.