I put a bunch of comments over on your Facebook album regarding this. The buckles in the quarters might pull out when the car is put on the frame machine to pull the rear (and front, likely) structure. But that hard kink in the trunk floor has me concerned... will it pull out? Can it be hammered back into pre-loss condition successfully? It's always hard to guess. You know it needs all parts for both bumpers, a rear body panel, frame rail repair at the rear and maybe the front as well, and the trunk floor is up in the air at this point, it is kinked over on itself hard, and it is ripped from the frame rail. If the quarter panel buckles do not pull out, that's more bodywork and painting (plus pulling out the quarter glasses for painting)... this is adding up quickly for a base model 2005 Cobalt, I have to say. *bites nails*
Which insurance does the other guy have? Not sure what the "rules" are for a PA resident hit in NJ by an NJ resident, insurance varies by state. I would be pressing for a rental car though, look at your battery, and with the trunk not closing, the car is not secure from thieves or weather. Plus it should be torn down to get a thorough estimate on the damages.
I would be checking your car's value on the NADA website. Check "clean retail", because that's what the insurance co will go by for value. NADA usually gives the most accurate value, but it is still a ballpark figure. The insurance company will place a value on the car, which you have the right to question.
It is going to be close. Good luck either way, Vipes, and keep us in the loop.
EDIT: when you go to the NADA site, choose "consumer", then "new and used car center", you will be able to go in and see.