I have used the 6MM Rem. on whitetails for many years with very good results! I would consider the .243/6MM to be the minimum caliber for deer. When I say " minimum" though, I am not saying that it is " barely" good enough. I am saying that with 100 grain bullets the .243/6MM is a very good minimum, for ANY whitetail deer or deer sized game.
I suspect that too many people, myself included, have fallen for the " bigger is better" craze! Todays thinking seems to be " hit ' em with an atomic bomb, and they will drop on the spot!" Wrong!
I would much rather see a well placed shot with a .243/6MM than a poor shot with one of todays latest, greatest, super-duper, dadgum-magnums! (Nothing against magnums, I shoot them too!)
Bottom line, I think that the 7MM-08 would be about as perfect a deer gun as you could get, power to spare and light recoil too! However if the .243/6MM is what you have or what you want, it will serve you well if you do your part.