Hi Mike,
The guys have given you some good advice here! As someone else pointed out, you really wont know what kind of shape the frame is in until you start removing the upolstery. Meaning, how are all the glues joints in the frame, any wooden supports cracked etc. If you were going to go through the trouble of tearing the whole sofa down, you could also inspect the springs as someone else pointed out. To rebuild the sofa properly, all that needs to be done.
If your lookin for the quick fix, I would try RobS suggestion and use the brown masonite trick, and you could also add a wooden block under the middle section especially if the frame has been undermined for extra support.
Im by no means an expert, but I have built my fair share of furniture, and at one time I did build some wooden frames destined to be upholstered furniture. I can tell you this, unless it started its life as an upscale expensive sofa, the frame is not much to look at !!!
Good luck.