As it is a web authentication method and not a mail one, it may never happen. Google's use has caused some debate, but there are strong feelings that Google's abuse of oauth should be ignored as it requires implementation of browser capabilities within non browser applications, a security issue for the applications.

You can follow the discussion in bug 840540

It is now a problem because Google's use of this protocol now causes a nag when starting Thunderbird to re-enter GMail your password which never gets accepted. The only thing you can do is hit cancel until it comes up again.

it may never happen.

Thunderbird 38 will ship with OAuth 2.0 authentication for Gmail accounts. https://www.mozilla.org/en-US/thunderbird/38.0beta/releasenotes/

It is now a problem because Google's use of this protocol now causes a nag when starting Thunderbird to re-enter GMail your password

I suppose the nag is for Google Contacts and you have the Google Contacts extension installed. The extension doesn't support OAuth2 and it seems it won't get updated either. You can disable the extension to avoid the nag though.