I use this setup. I've got a 1500 watt inverter hard-mounted in the Jeep which happily runs one of the 3.5 gallon Porter Cable pancake compressors. More output than any 12v compressor I know of (2 SCFM at 90 psi). They make a slightly bigger version with similar power draw too. Given very light use or a bit more tank capacity, it's enough to run an impact gun in addition to airing up tires. The compressor doesn't seem to run any differently on the modified sine wave power from my inverter than it does plugged into any other source of 120v.
I don't have mine hard mounted in the Jeep, I just bring it with me when I'm traveling somewhere I think I might want / need a source of air. For a good portion of the Jeep's use (DD-ing, trips on paved roads), the compressor stays home.