I seriously doubt that any of the cheap inverters will drive a compressor. They may advertise the rating in watts to run it, but i seriously doubt they can handle the surge required to start an electric compressor.
I predict crash and burn at worst, blown fuse on the car or thermal overload on the inverter at best.
Even a DC compressor capable of filling tires in a reasonable amount of time requires around 30-40 amps DC supply. Each and every connection or conversion looses capacity as none of them are 100% efficient.
If it plugs into the cigarette lighter, you won't be happy with it filling the tires on a 2500+ series pickup.
I could be wrong, but I would be shocked.
I wish I had some better news, but being only 1 beach that I go to has air, I have been down this route already.
Engine driven, hard wired DC or tanks of pressurized gas are the only options unless you have a lot of patience and time.
The Pickens Plan
"Democratic civilization is the first in history to blame itself because another power is trying to destroy it"
- Jean-Francois Revel