I think it's one of those mysterious American slang expressions that didn't really arise from anything in particular, but rather somebody said it (either intending to say something else, or just to say something different), and since others still understood the intended meaning, and presumably liked the sound of it, they started using it too.
It may be a variation (intentional or un) of "jammed up" which was popular over here around the turn of the century -- the most recent turn, I mean.
What's a "tyre?"
