OK, my problem with my webmail and my [Thunderbird] user are fixed. Here’s what happened. When I was setting up my server install with the AppleCare rep on the phone he said to check CRAM-MD5 and Plain for authentication. This inside of Server Admin.
It turns out that the default authentication method for SquirrelMail is login so out of the box it needs to be checked. I think, though I cannot confirm, that it might also be the default authentication method for Thunderbird.
You can change the preferences in SquirrelMail using the following command.
> sudo /usr/share/squirrelmail/config/conf.pl