Dude a 6D isn't truly going to help you out much at all. It's not like full frame brings you into a new photographic dimesion of instant awesomeness to beheld by all the peasants below.
Honestly, just borrow a backup body from someone. Even a rebel. Whatever. Just use it only in emergencies. Save your money because it will help you out a helluva lot more by getting more glass.
I'm gonna be blunt. It's your first wedding. Things are going to happen faster than you can react. You gotta ensure a solid set of reportage photos first, and artistry second. Leave the primes in the bag for now and grab a zoom like the Canon 17-55. I've been shooting weddings professionally for 14 years and while I've shot mainly primes for the last 23 years of photogrpahy, I still use the 17-55 often because it helps me keep up with the action.
Put the camera on P (Program) mode and worry just about ISO and turning the flash on or off. Only two things to worry about. Forget M and Av for now. Otherwise, I can almost guarantee you're gonna shoot indoors at like 1/4 and blur out a whole set of photos, or shoot in noon day sun at ISO 1600.
You are already probably a master of your 60D. It is MORE THAN CAPABLE of shooting a wedding with the highest standards of quality. Honestly, shooting a newer body while you're already confused on the day is just bad news. You gotta keep it simple for your first wedding. The more complex you make it, the higher the chance that you'll screw something up. I still shoot weddings with my 40D, and it is fantastic.
Of course, if you just came here because you wanted us to justify an excuse for you to get a shiny new body, then do whatever you want and get the 6D. (But you'll probably do a better job with your 60D)