I posted a few weeks ago that I tested all of the appliances on the 'pod, and the A/C uses 1000 watts continuous, fan on low and compressor on. What I was using to measure wasn't fast enough to catch the starting surge but I just can't see a 3 kw genset not handling it. By your description it sounds like your compressor is bad. Have you tried running it from your house? If its good, you'll have no problem running it from a 15 amp outlet (with an adapter).
Note that we've tripped the power pole breaker when we've tried using the microwave, A/C and the electric element on the water heater all at the same time. About right, since just those 3 together adds up to 4 kw with my measurements (plus add a few lights, the fridge in AC mode and you are up to 4.3 kw). Way over the 3600 watts a 30 amp breaker will handle.