I enabled two-factor authentication on my Google account today, and the change caused my chat client to lose access to my Google Account (I use Messages.app on OS X to connect to Google Talk). When I enabled TFA, Messages.app showed this message:
Messages can’t log in to email@example.com because your login ID or password is incorrect.
Entering my Google Account password did not resolve this. It turns out that enabling TFA causes Google Account passwords to no longer work with Apps. You must instead setup and use App-specific passwords, which is done using Google’s App passwords page.
In my case I had already entered my Google Account password into Messages.app (as opposed to the Google generated App-specific password), and been denied access by Messages.app. This tripped things up. Messages.app continued to reject the now correct App-specific password another half-dozen times. If Messages.app has already rejected your password, try restarting the app and re-entering the correct App-specific password. That seems to work smoothly.
In summary, if you enable TFA on your Google Account you’ll need to create App-specific passwords for your apps to use to connect to Google services such as Google Talk:
- Enable TFA on your Google Account (Sign-in & Security page).
- Generate an App-specific password for Messages.app (Google’s App passwords page).
- Quit Messages.app, re-open, and paste the App-specific password into the dialog when you connect.
Hope this helps.