It turns out that the pump in the ejector pit has been running continuously. Now this does beat the heck out of "not running at all", but it's just not a good thing, especially when you put your hand on the PVC pipe leading to the sewer and note that it's distinctly warm.
Gretchen called the plumber that we most recently used to clean out the pipes leading from the kitchen sink to the street. It turns out that it's $600 to replace the switch assembly on the pump which would then probably continue to work for some unspecified time or $1000 to replace the whole pump.
I've voted to replace the whole pump. It's nearly eleven years old and I really prefer to have it working. And I really prefer not to be dealing with the ejector pit myself, given that I know what's getting ejected.