Swedes have killed millions of moose/reindeer over the years with the 6.5X55, I expect it would be fine for just about anything in North America, short of Grizzly Bear.
I have a LR Varmint/Target rig in 6.5-06, built on a Rem 700 Action, with a 28" PacNor heavy barrel, in a HS stock. I shoot Hornady 140 AMAX (@~2800) for P-Dogs, and Sierra 140 Matchkings (@~2900) for target shooting. It is by no means a lightweight. It has easily 1000 rounds through it, and so far no drop in accuracy. I took it to the range last Saturday and was hammering steel plates at 400, 500, and 600 yards with ease, and once I figured out the dope, was hitting a steel plate at 950 yards about 3/4 of the time. I killed a P-dog at about 850 yards with it a few years ago. It is really a wonderful rifle.
It is a heavy S.O.B. though, and I wouldn't want to have to carry it all that far.