Connecting Adium to Google Talk with a 2-factor authentication account isn’t working

Try using the password generator in gmail settings. When you type in the name of the application it generates an application specific password. However, in the box you should not type in 'Adium' as your application name. Instead, you should put "GoogleTalk/Pidgin" as your application name. Paste the generated password in your adium login and you will be set!

Check out this link:
http://help.trillian.im/discussions/web-questions/25-google-talk-login-widget-not-accepting-my-new-passwords

Specifically, they mentioned going to:
https://www.google.com/accounts/DisplayUnlockCaptcha ..and then trying to sign in with your client.

They also recommend creating a new application password and ensure your client hasn't cached your old one.

The specific answer for my original question is that I have an unsupported setup in trying to use a 3rd-party chat client without a Gmail account associated with my Google account. This was pointed out to me by an Adium engineer and is detailed on this Google help page:

https://support.google.com/chat/bin/answer.py?hl=en&answer=159495