the 660 no, my brother has a 660ti in his computer and can't manage 60 with ultra settings.
the 670 is different, i would recommend that, as it runs ultra at around 60 (i think 57 is it's average) with ~70 being it's max, and ~45 being it's lowest
you can do even better for $100 more then the 670 and hit up the 770, which is described as "a 680 on steriords"
so for ultra at 60, i wouldn't go less then the 670
its the weird thing with nvidia, the x60's are always not enough to max out the most demanding games, but comes close, then there is a huge performance gap between the 60 and 70, and the 70 may come out to be too much for what you need. Or at least thats how it's been since the 400 gen.
however if you turn settings down on things that during a firefight you wont pay attention to, like AA, lighting method, possibly shadows. then a 660ti will suit you fine