The answer was a simple one once I figured it out. I disabled all the Google Labs and it magically started working again. I then re-enabled Labs until I found the one that was causing the 707 error – the “Background Send” Labs. Apparently something broke over the weekend with Background Send and the newest browser version of Gmail.
If you are getting a 707 error, just turn off Background Send. That should fix it.
Thought it might be useful to some.