My 600 watt ballasts are rated at 5.5 amps, a standard outlet is wired for 15 amps. However, ideally you don't want to use more than 80% of the max amperage. But 5.5+5.5=11, 11/15= 73%, so you can safely plug 2 600 watt lights into a standard 15 amp outlet.
However, make sure you know what breakers each outlet is connected to! A typical bedroom will have a handful of outlets, but you need to know if all of the outlets are connected to the same breaker or if they are on separate breakers. If your room has three 15 amp outlets, but they're connected to the same 15-20 amp breaker, then that means you can only use 15-20 amps total on all three outlets.
Take a look inside your breaker box and try to get a good idea as to what outlets each breaker goes to. If you're in a standard home, you'll likely need to have 2 lights per room to avoid tripping breakers or worse, fire. This is because each room in a home is typically wired for 15-20 amps total.
I don't know if you have a garage, but take a look at what breakers go to your garage. It's not uncommon for a garage to be wired for more than the standard 15-20 amps because a lot of power tools can push 10-15 amps all on their own.
Using only 80% of the total amperage is important because the ballasts/lights draw more juice than normal when they first kick on, by not maxing out your breakers you will be able to account for this no problem.
Be safe and if you have any more questions this is the place to ask
