A craftsman mower did not start at all. I cleaned out the carburetor, cleaned the passages on the bowl bolt. The air filter is clean, the fuel drips in a 1/8" stream without the bowl attached. After all of this, A few pulls will get the engine to start, and it has run as long as ten seconds or so before dying with a puff of blue-ish smoke. The spark plug has a .03" gap but looks a little oily. I cleaned it up with little change in behavior.
I had a similar issue with my Craftsman mower. Turned out the needle valve was sticking. Once it started, I could tap the side of the carburetor with a small hammer and it would then keep running. Replaced the needle valve and it's been running fine all summer.
Unless you're absolutely sure that your fuel tank contains 100% fresh new gasoline, drain the fuel tank completely and fill it with 100% fresh new gasoline. If that fails to do the job, check the needle valve - you may be able to clean it if it's sticky, you may not.