Experienced the same problem with my 1993 Tacoma pickup. Luckily I was in a tire shop at the time and asked them to take the spare tire down. It took them quite awhile and effort to pry the cable and tire down with some deformation of the mechanism. A good spraying of Rust Reaper might have worked if we had some at the time.

Toyota has since replaced the cable with a chain mechanism which doesn't seem to freeze up like the cables did. At least I never had the problem over 265,000 miles with my 1996 Tacoma. The chain mechanism always worked the few times the spare was needed.