So I went to the bike shop instead, and got two new inner tubes (one for backup!). Then I dropped off my ballot and changed the tube. This is the first time I've changed a tube on a bike. It wasn't difficult, but it required more strength than I was expecting. Also I had a little trouble getting the wheel properly seated when I put it back on (I've not removed the rear wheel before, either), but it is all better now.
I don't think my hands have ever been that dirty before.