Looks like my fat ass wore through my first rear tire.
I bought a couple of these:
Continental Tour Ride Urban Bicycle Tire (700x32)/(28x1 1/4x1 3/4)
The guy at Big Wheels told me that 700x25-30 tubes would fit, but I didn't notice at the time that this was "outside" the range. Am I good with these tubes? They inflated just fine and feel ok, but I don't want to take them out on the road if there is a problem.