I too ran into the same error – “Daily Limit for Unauthenticated Use Exceeded. Continued use requires signup”.
I went and checked my google developer console under APIs for the project associated with the API key/ auth key, eg,
https://console.developers.google.com/project/<your app id>/apiui/api. The status for Google+API was set to OFF. I turned it ON.
I then got another access token, and then tried with the new one. It worked, ie, the error was gone and I got the profile details. To cross-check if that was indeed the cause of the error, I went back to console and disabled Google+ API. But now, I get the error:
“Access Not Configured. Please use Google Developers Console to activate the API for your project.”
So, I am not 100% sure that it was the turning on/off of the Google+ API in my developer console, but do ensure that this is turned on. Also, wait a few minutes after turning on, and ensure that you get a fresh token each time before trying it.