I saw some apps not responding, so I tried to sample the processes (so I could hand the data off to a more savvy friend). Note that in neither of these screen shots was the cursor over the highlighted Time Machine Menu Bar item; I'd clicked on it in an attempt to suspend backing up, in hopes that that would lessen the load on the poor laptop, but that just made things worse. The whole thing started when iTunes wouldn't launch, so after a few minutes of the icon bouncing in the Dock, I used Activity Monitor to get it to quit. The next dozen times I tried to relaunch it, there was that lovely error message.
The computer sat like this, with eventually the Finder being unresponsive, for 10-12 minutes before I forced a reboot.