The carb may be draining into the engine, make sure to check this since the fuel can get past the rings and into the oil.
Alright, if this is the case, how do you fix it? I seem to have the same problem as the OP. Generally on a cold morning, I'll pump my carb 6-8 times and it'll fire off and run fine. I don't seem to be having fuel get past the rings into the oil though.
