Eyedropper works pretty good too to squirt gasoline into the carb.
Trick my friend told me for a gas powered pressure washer that ran bad was to cover the intake with your hand a few times. Idea is that the extra suction caused by blocking the intake will clear out a clogged pilot jet. We got lucky and like some small motors the pilot jet pops out in seconds for easy cleaning. So i never tried that trick.
But its not a bad idea for the generator. If you can get it running try putting a piece of cardboard over the intake and kill the motor. Might get lucky and clear up whatever is clogged.