Which version of the plugin are you using?
I just tested it and I cannot replicate the bad authentication issue. Can you please try with our online demos?
g_c 2.11
OK, problem solved, I guess.
Google kept thinking my account was being hacked so it force-changed my password every attempt. I finally sorted it out by going to this page:
http://support.google.com/mail/bin/answer.py?hl=en&answer=14257&p=client_loginwhich in turn led me to item 3 in the list on that page:
http://www.google.com/accounts/DisplayUnlockCaptchaand it gives you a ten minute window to sign in the with google_contacts setup.
The README for this plugin needs an explanation about this potential I think.
Thanks for your patience!