Sunday afternoon, I met with several friends to do a 28 mile ride. One of them recommended a shortcut through the school grounds, less than a 1/2 mile from the starting point. As soon as we left the pavement we realized that we had ridden through a patch of some sort of thorny ground cover.
I started pulling thorns from my tires (about 10-15 per tire), and heard a hissing sound with every one pulled. 3 of my friends had the same results. 2 of them (including the one that recommended this 'shortcut') somehow didn't pick up any thorns.
We walked back to the house, I called my wife, and asked her to bring one of my other bikes over so that I could salvage the tubes from it.
We found just enough spare (and salvaged) tubes, and still had just enough daylight to complete the ride, so it turned out to be a nice day anyways.
Lessons learned: No more shortcuts. Always carry spare tubes (I always have one...but obviously that wasn't enough).