Or, more specifically:

Is the car jacked up and supported by the frame so the suspension is hanging freely? In other words, you're not trying to compress a shock that's already fully compressed, right?

Assuming that's not it, how about taking a big screwdriver and prying the bottom mount up and out of the lower control arm. If your suspension was working, the shock MUST be compressible and you only need to compress it enough to get it out.