The annoying: After this happening about six times, I figured it was time to move the bungee cord.
The ugly: Somewhere between Yuma and Blythe I pickup up something about the size of a railroad spike. And didn't notice until I was driving on the sidewalls. And the tire stores are closed until Tuesday. (Not that I had to be anywhere before then, but still.) I mounted the spare, so now I'll just chill for a few days.