Eventually, it occurred to me that maybe somebody got a Discover Card in my name, so I checked my credit report, but no, nothing was wrong there.
So finally I decided to call the number back after I got the 3rd cryptic message left on my answering machine.
The good service part: I got to a Discover customer rep who pretty efficiently figured out that they had the wrong phone number. They were looking for a different person in a different town who had the same name as me. The rep immediately said she'd make sure my phone number got removed from the account. Assuming that in fact the phone calls now stop *cross-fingers*, I was somewhat surprised at how easy it was! Considering the horror stories I've heard about dealing with customer reps, I expected all sorts of hassle, but it was no problem! :-)