I've verified that the cron job is running properly (every 5 minutes, for which there was no mention of how often to run the job in the 1 line of documentation I could find). I have also verified the server clock time and have tried scheduling everywhere from 10 minutes to 24 hours in the future - nothing. Any suggestions on how to debug this?

I found the cron instructions to be incorrect and fixed them by changing the cron command to the following (Replace: YOURSITE.com with your actual domain):

wget --user-agent="Browser" -O /dev/null "www.YOURSITE.com/index.php?option=com_rsmail&task=cron"

This does a better job of simulating a browser visit to the URL that triggers the cron job.

If it still does not work, try triggering it manually by visiting:
www.YOURSITE.com/index.php?option=com_rsmail&task=cron

If that works, then there is a problem with the cron job - it may not be running at all. If that does not work, there is a problem either with RSMail! or your Joomla! installation.

Hope that helps someone out there