Plugin could not be compatible with two-step verification. Plugin have to login to your account in order to make a post. 2 step verification requires entering the code from your phone. Plugin can’t take a look at the screen of your phone each time it needs to make a post, so it’s not possible for it to login like this.

Also plugin could not be compatible with “application specific passwords”. Application specific passwords could be used only in the non-browser applications, but Google+ is accessible by browser only.

If you are concerned about your personal Google account and want to keep 2 step verification on, just create another account, make it admin for your Google+/Blogger page and use it for auto-posting.

UPD: Link to “Owners and managers on Google+ Pages” –

UPD2: There are no “workarounds”. The whole idea of two-step verification is to prevent an access to your account from anybody without your phone in the hand. What would be the purpose of such protection if you can go around it?