So, you're saying it stopped and will not restart at all?
Well, it could still overheat, even if it has a good stream. Say, for example, the thermostat got stuck closed.
Ignore this if you've already checked it but could it be something simple like:
The fuel tank vent was not opened.
The fuel hose is sucking air.
The fuel pick up tube in the tank is broken off.
I know you said it was getting fuel but it never hurts to double check.
You are certain it's getting spark? How are you checking for spark? Do you have a charge kit and were you hooked to and charging a battery when it stalled?
You could be right about some debris getting in the carburetor. Do you have a way, other that the dreaded, engine killing starting fluid, to provide another fuel source? DO NOT USE ETHER STARTING FLUID!! It will damage your engine.
Propane from a soldering torch works well. Or carburetor cleaner spray "fogged" into the intake will make the engine run briefly to prove a carb is not supplying fuel.
Maybe someone else will jump in with some better questions and/or answers.