The problem has been identified and the mitigation work is underway by Google team. The performance of the authentication service is improving.
Google Team has also reported that some users were able to log in using an incognito window under the Chrome browser. Here's how to switch your browser to the Incognito mode in Chrome: https://support.google.com/chrome/answer/95464
NOTE: You are still able to login to your Ecwid dashboard at https://my.ecwid.com
by typing in your login and password. You can also manage your store via our mobile apps on iOS or Android.
Further updates to follow.