Every NTSC TV that we've ever seen as consumers will play back a 60fps game just fine. This includes old 480i CRTs. Europe capped at 50hz for a long while, but 60hz is also common over there now too.
In example, take Rage on the Xbox 360. It's a native 720p game, and runs at almost a perfect 60fps. 720p is a progressive format (hence the P), that runs at 60hz. This means you get a full frame every 1/60th of a second, or 60fps. For example sake, let's set our 360 to spit out 480i. 480i is still a 60hz signal, but it only updates half the image every 1/60th of a second. The result is that at any moment in time, half of two individual Rage frames is being displayed on screen. Our human visual subsystem is pretty sloppy, so this looks a lot better than it sounds like it should and still results in a full 60fps display.
Stepping up to 120fps on 120hz displays? Only if the TV specifically says that it accepts a 120hz signal, which is still exceptionally rare. A 120hz TV LCD for example still maxes out as a 60fps display when it comes to gaming.