By this evening, there was a small pool there, and soaked carpet extending through three rooms of the house. The plumber was summoned.
Apparently the hot water line that goes from the water heater out has come apart somewhere inside the concrete slab it penetrates on its way out. This has required turning off the hot water until tomorrow, when a couple of guys will show up and run new pipe around said slab to replace it. One could jackhammer the concrete away and fix just the bit of pipe that failed, but this is apparently a stupid thing to do because then the rest of the pipe will die bit by bit anyway. Go go gadget homeowners insurance!
In related but different news, Livejournal is sending me some, but not all of my comments in email. So if I don't respond to you I am more likely to be ignorant of your response than ignoring you.