It fires right up but only runs for a few seconds and acts like it is out of gas. Does the small unit in gas cap that holds fuel stabilizer have to be full. Would this cause it not to stay running?

Hi
Sorry to hear of your problems, but the fuel stabilizer in the cap will never be full. Just not that way. You have a fuel restriction. It is probably caused at the inlet needle and seat in the carb. General cure is the #398188 needle and seat kit. Old seat can be extracted with a #5 crochet needle; new one can be put in with the other end of the needle(the side with the groove is not to be seen, goes in first)
Easy way to tell if this is needed; take the carb and turn it upside down; if the float is not level, there you go!
Peace,
Clarke