I think I've got it nailed down a bit. When I run the nVidia drivers it is not using OpenGL. The Google Talk plugin needs OpenGL to work. I can force OpenGL to run. The the talk plugin works but Firefox will not run. If I switch to the Nouveau drivers then OpenGL will work fine without any messing about but again Firefox is unhappy.
So for right now - with my GeForce card my choice is Google Hangouts or Firefox.
I don't do the Hangouts that often. I may try just switching over if I need to. I usually have my little Windows laptop at my desk. I don't use it unless I need to go to a meeting but I could hop over to it for video chats if I don't have time to switch my graphics over on the Linux box.
It's not the greatest situation but I do feel better now that I feel like I have a grasp of the situation at least.