Small Engine Troubleshooting Problems? Ask a Mechanic Now.
You are correct in your thoughts. I would recommend that you clean the main jet in the carburetor as it will get stopped up periodically and cause this problem. When you choke or prime it you are bypassing the main jets and forcing fuel up into the throat of the carburetor, if you continued to push the primer once the engine starts you could most likely keep it running for a little while although it may not run properly. From what I can tell it looks like you have a Tecumseh engine on this machine. When you go to clean the main jet all you need to do is remove the bolt/nut that holds the bowl on the bottom of the carburetor and inspect and thoroughly clean the holes that are in it(3 or 4).
Can you verify the engine brand for me?
Okay, the bolt or nut that holds the bowl on the bottom of the carburetor actually has the main jets in it. There will be either three or four small holes in it that serve as the main jets. All you need to do is remove the bolt/nut and thoroughly clean those holes. A small needle works well for helping to remove anything that might be in the holes and then follow it by spraying carburetor cleaner or blowing air through them. This should solve your starting/running problem.