Running A/C with extension cord into 20 amp outlet.

Running watts is one thing. What really kills things is the inrush current when the compressor starts.

If I were doing this for the long haul, I would buy a Magnum Energy Hybrid inverter, just so the A/C's locked rotor amps hit the inverter and battery, which can easily take them, as opposed to a 15-20 amp cord which is not going to like even a brief period of handling 60 amps.