So, you've installed your new Fedora 19 system and want to synchronise mail, contacts and calendars with Google and chat on GTalk? To do this you traditionally go to system settings and do this in the 'Online Accounts' section (pictured above). Well, at the moment it won't work out-of-the-box for everyone.
This bug generally only affects those of us who use two-factor authentication (you should too!). Basically your sign-in and authentication will go through fine, but seconds later you'll see the 'credentials have expired' notice you see above.
However. this can quickly and easily be fixed. In your Gnome Shell search bar search for 'Seahorse' and a tool called 'Passwords and Keys' should appear. Load up this window and you'll see a list of keys. Look for the one that starts 'GOA google credentials'.
What you should do is (after generating an application-specific password in your Google Account settings) check the 'Show password' box then scroll along the password field until you find the 'password' section.
Simply change the password value on the right from your ordinary Google login password to your newly generated application-specific password.
You should then log-out and back in to your system (you can just close all windows and re-open them, but logging out is quicker!). When you return to that settings panel you should have resolved the problem!
Please note: This issue was still active at the time of writing. If you are reading this some time in the future the issue may have been resolved.