H-m-m-m. Interesting how so many people have had slightly different experiences with this. I remember the days when this was considered a sign that the software was not ready for release, and the team would actually fix it BEFORE users started seeing these problems:(
My own experience was just a little different. I had already tried Project>Clean, but still got the same build failure. Then I deleted the debug.keystore (under .android) just as the first answer said. Still got the same problem. Then I did a clean again, and wonder of wonders, it worked!
Now don't get me wrong, I am glad that I got it working thanks to the hints in this thread. But clearly clean isn't working right, and how did it find an expired key after I deleted the keystore??? Clearly something is wrong with Eclipse or the ADT -- not so sure which.