Power inverters work well for low wattage devices but they draw a lot of current for higher wattage devices. If a 120vac compressor drew 10 amps from a 120v wall outlet, it'll draw over 10X that amount at 12vdc. In other words, it'd require well over 100 amps from a 12 volt circuit.
To produce the same work at one-tenth the voltage, you need 10x the amperes.