Lesson learned the hard way:

Do not put a plastic shipping envelope in a shredder, no matter if it looks like it will go through or not.

I got the shredder working again, but it took two hours of using a knife, scissors, a screwdriver, and a pair of tweezers to get all the little shreds of plastic unwound from around the blades.

And I still have a pile of old papers to shred.

I won't be making that mistake again.