Mac Mail can't send outgoing messages via GoogleMail
There appears to be a problem on Gmail's side with their SMTP servers. This seems to have afflicted all non-browser based email clients that rely on SMTP and is apparently affecting a large number of users.

By the looks of this thread, it appears that they are actively working on a solution.

I think for now, all we can do is wait on google to hopefully fix the problem on their end.

Update: the issue has now been resolved and outgoing gmail should work through Apple mail.