A power inverter of sufficient rating should have no problems at all driving that setup. The question I would have is why you wouldn't just plug it into your car stereo. There are tons of ways to get your iPod or other portable MP3 player into your car system. Then, use the speakers when you need them other places.
If you want to run the speakers outside of the car, but still powered off the car, then perhaps consider building a speaker box that plugs into a car amplifier. You will be able to integrate that right into your car system seamlessly, and, if properly built, can be moved on long wires outside of the vehicle as well.