Inrush current would be a problem. Takes a lot of I to get the compressor churning. I have a 1000w inverter to run my electric chain saw which is rated at 7.5 amps. Sometimes the circuit breaker trips when I push the go switch on the saw.

The less expensive inverters produce a modified sine wave. Be sure what you buy can run off the modified sine wave. Some devices will not work, or won't work properly. Ask first.