I have resolved the issue. It looks like several people were having this same problem so hopefully this helps someone else.
The tutorial says to put the line:
PARAMS="-m /var/spool/postfix/var/run/saslauthd -r"
in the /etc/default/saslauthd file. However I looked at The Perfect Setup tutorial for Debian 4.0 and it suggests not adding that line, but rather modifying the Options line in the file like so:
OPTIONS="-c -m /var/spool/postfix/var/run/saslauthd -r"
I made that change, restarted postfix and saslauthd and sasl authentication is working perfectly now.