4400's were the ones that used the Chevy engines. The 3300's had 4 cyl Deere engine.

When it sputters is it blowing black smoke or no smoke? If blowing black smoke it is running rich and I would suspect carb. These were bad about the needle valves sticking and flooding the engine with the electric fuel pump. If it is n ot smoking black one other thing to check out is make sure a soybean or other obstruction is not blocking the fuel tank outlet. Make sure a good stream of gas is coming out of with the sediment bowl off. One ont so uncommon thing to happen is an operator forgetting to put the gas cap on after refueling - and junk gets into the tank and causes problems till it either works its way through or gets cleaned out. Just a couple of other suggestions.

Check the coil, points, condenser, plug wires like has been suggested.

John

PS; for future reference, if the carburetor needle valve ever sticks and floods the engine, take the hose off goint to the carb,  let the gas run out (be fire conscious), unplug the electric pump, and start it up - plug the pump back in.