Why is com.google.android.gsf.login warning me that I need to install Google Play Services?
I have had a similar issue on my Nexus 4 device, here is what I did to stop the issue:

Go to your 'Settings' menu, then go to 'Accounts'. Select 'Google' and check which google service has a sync issue. If you cant see any apps with sync issues, you will have to do as user 'Laural H' mentioned above: disable them all, and re-enable them one by one, checking that it syncs properly (before enabling the next one). When you find the app with sync issues, open the problematic app and login with your google credentials.