The same thing happened to me, for the first time in the two months that I've had KitKat, over the weekend. It happened to all five of my Google accounts, and the Motorola ID thing, which I had just set up a few days before - and it happened when I was in a restaurant and, from the battery history screen, I had no mobile service. (I didn't look at my phone until I got home from the restaurant.)
Since it never happened before I did the Motorola ID thing, I first had to reenter the passwords for all of those Google accounts (retrying did not work) and then I unlinked the Motorola ID from the phone.
So, that was:
settings->security & screen lock->Device administrators and turned off "Motorola Device Policy". Next, settings->Motorola Device ID, tap the three dot menu control on the top right, and choose "unlink account".
It might not hurt to restart the phone, too.
Since it never happened before I did the Motorola ID thing, I first had to reenter the passwords for all of those Google accounts (retrying did not work) and then I unlinked the Motorola ID from the phone.
So, that was:
settings->security & screen lock->Device administrators and turned off "Motorola Device Policy". Next, settings->Motorola Device ID, tap the three dot menu control on the top right, and choose "unlink account".
It might not hurt to restart the phone, too.