Seems like some people are experiencing this problem, and I haven't read anything definitive about it. You're using the latest Google calender sync (0.9.4.1)?
I enabled 2 step verification and used that password in Outlook. Now I get this error
Since I use Outlook on my registered computer I figured it must not need the special password but the regular one, so I changed it to use my regular one and I still get it. Google's instructions were not to write down the password used for two step verification so I have no way of entering it back into Outlook.