Are you able to log-in successfully to other Google services e.g. Play Store, Google + etc? If so then I suspect that an authentication failure in a single service is a server-side error which will (hopefully) clear itself in time.
Droid 1 had this error when did factory reset last week. Went through various forums, tried many things, but what did it was changing Google Hangouts setting to "revert to old chat".
It works now.
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