Inverters draw alot of juice. Remember that wattage = amps X volts. So if you are drawing 800w at 12V, that means it will be sucking at least 66.66 amps per 800w inverter at full draw. Plus, you have to figure in that your inverter is not 100% efficient, so it's not unreasonable that it could draw as much as 100 amps at full draw. At this point you are approaching the capacity of your alternator. So for our purposes, let's just say that your alternator will be good for about 100A (will give us a 25A safety cushion for the vehicle's electrical draw-onboard computer, etc).
Now, it IS possible that you could run two 800w inverters at once knowing that you would draw down the battery at the rate of 66amps. So, if you figure that a starting/deep cycle group 24 battery will have only about 90 amp/hours of storage capacity (on the generous side), that means you will draw the battery down to 50% charge (electrically "dead") in about 40 minutes. You would then need to shut down the inverter long enough to charge up the battery again. So assuming again you can put 100A back into the battery, it will take you about 30 mins or better to charge the battery back up (maybe more). So you're looking at 40 mins of on time, followed by 30 mins of off time. That gets you about a 75% duty cycle using both inverters at once. Not bad, but not great either. I'd say you could probably run one 800w inverter constantly and be OK.
Above it was mentioned about the phase of the inverters, and having them fight each other. This is partly true:
The input (the "draw") for the inverters from your 12v system is DC - direct current. Two inverters can connect to the same 12v source no problem - the current does not alternate, it flows the same direction all the time, so there is no "phase" difference to worry about.
The output (the 120v side) IS alternating current - 120v, 60hz. You CANNOT plug the outputs from both inverters into the same circuit, but you can run the inverters individually. In other words, if you fab up a way to plug both inverters into the breaker box on your home, you ARE going to have problems and probably blow up the inverters. However, you CAN run an extension cord from inverter #1 to your TV, and another SEPARATE extension cord from inverter #2 to your satellite reciever, and you will be good to go. But if you somehow gang both inverters together into the same power strip (or other circuit), bad things happen. Think of it like one proton pack with two "guns" attached. It's OK to run both guns off one proton pack, but DON'T CROSS THE STREAMS!
Clear as mud?