Similar issue here but mine is specifically with a Google (Apps) for Education account. We have SSO enabled (not sure if that matters though) After installing 10.10.3, the following behavior occurs:
When adding a new account, if I select the Gmail, a window pops up with what now looks like Google's normal web authentication sign-in page. I enter in my credentials and I get redirected to my school's shibboleth SSO. Even with the correct credentials I get that "failed to authenticate with Google" error.
I can get around this issue and still add an account by selecting the "Add Other Account" option. In this instance it by passes the SSO and I can use my Google Apps username and Google Apps password like prior to 10.10.3 to successfully add the account. The problem is, even after I am sending and receiving just fine, any time you go into System Prefs > Internet Accounts and click on the Google Apps account, it keeps trying to authenticate me via my SSO and gives the "failed to authenticate with Google" error when I put in the correct SSO credentials.
Are you guys that are having issues with 2-step, using regular Gmail.com accounts or are you also on Google (Apps) for Education/Work? For the ones with 2FA issues, have you tried adding the account as "Add Other" to see if your app specific password words there?