The tire inflation warning which we got almost immediately upon getting on the freeway the first evening turned out to be an actual problem. The next day (Thursday) we took the car to Saturn in Santa Ana where they determined that the tire pressure really was low. Assuming that we had run over something, they simply repressurized the tire since it is supposed to be self-sealing.
However, that evening, we again got the low pressure warning and so again on Friday, we took the car into Saturn in Santa Ana. This time they removed the tire and found that the valve stem had a small hole in its base. This looked like a problem with the original mounting of the tire on the wheel.
We weren't happy that we had a problem (especially one which appeared to be a manufacturing quality one) so early in the game, but at least the Saturn service lived up to its name, and now we know the tire pressure sensing mechanism really does work.