This was discovered through trial and error, rather than through web searches... so for anyone who's run into this problem, here's what worked.

First, the problem.  I recently reset my iCloud password.  I was foolish enough to have my account set up for iCloud logins.  This... was a mistake.  After I changed my password, iCloud pushed a password update to all my computers... a broken update.  In other words, I lost the ability to log in or authenticate to anything.

Take note!  If you have iCloud login enabled, disable it or risk being hosed like this.

Now the fix.

1. You'll need a bootable USB key or flash disk.  You can use the hackintosh boot disk creator over at tonymac to create one of these.  You may be able to use the recovery partition (hold down cmd-R while starting up)... but this seems to have mixed results.  It works on some hardware configurations, but not on mine.  Either way, you want to get to the installer/recovery partition boot screen.
2. In the Utilities menu, choose 'Terminal'
3. Type resetpassword without the quotes.
10. Back in the terminal window type reboot without the quotes