Honda GX690 starting problem

My Honda GX690 starts occasionally.  When it does start, it seems to run fine, but if I shut it off, it won't start again.  It cranks over but will only fire up when I pour a little fuel in the carburetor.  I have checked the fuel shut off solenoid and it seems to be working fine.  I replaced the fuel pump and fuel filter because even though I thought they were fine, they were pretty inexpensive and it seems like its a fuel delivery problem.  The pump does pump fuel when I crank the engine.  I did check the plugs for spark and replaced both plugs(correctly gapped, of course).  I've gone through the troubleshooting in the repair manual, and I just don't know what I'm missing.