I believe that in a SHTF scenario like you speak about (And I consider confiscating all weapons a SHTF scenario) that many police officers would simply refuse to enforce the laws or resign. I know I would.
I know that LEO isn't the only place this would happen. How many military members are gun owners? I plan to be, and would do what little I could(consiencous objecter most likely). They'd have to institute a draft to keep the numbers up, and even then they'd have trouble.