I am running WP 3.6.1 on PHP5.4, and the plugin installs fine.
If I use the OAuth method-
I enter my Google login, get redirected back to the settings page with a "Authenticated" message, but the page looks the same (no options).
If I use the old method-
I enter my Google login, get redirected back to the settings with a "Login Successful" message, and I get the options list. I can select my desired options, but when I click "Save Changes" I am immediately redirected back to the initial login page.
In either case, the dashboard always displays the message, "You need to log in and select an account in the options panel."
I tried logging in the old way and checking forget everything and forget authentication options (together and separately).
I also removed and re-installed the current version.
This plugin used to work.