I found a work around for Gmail with two factor authentication enabled that works for now...but i'm not sure how long it will last.
1.) Open Mail/Preferences
2.) Select Accounts
3.) Enter Gmail password (should not be any password listed for 2 factor authentication accounts)
4.) Save settings
5.) Restart computer
6.) Open Mail/Preferences again
7.) Select accounts
8.) Delete Gmail password
9.) Save settings
10.) Restart computer
This has been working for 24 hours for me now on both of my Gmail accounts. Hopefully this will continue, because removing and re-adding the accounts would work temporarily, but once the computer was restarted, I would lose connectivity with Gmail servers. The above directions have gotten me through numerous restarts so far, and all is working.