ryan790,
This could be either electric (ignition) or fuel and it sure sounds like fuel to me. If the carburetor can't maintain fuel at the proper level, it will just slowly kill the engine. Usually an ignition problem is instantaneous, just like you shut the key off. Because it backfires, it reinforces the theory of a starved carburetor.
If you can get it to do it's thing, then before it has a chance to recover, dump a little fuel into the air horn and see if it roars to life. Watch out for back fires and barbecues.
Old fuel tanks and old rubber lines can cause problems like this. Do a little more sleuthing and see what develops. Does this sound plausible?
Stuart