Thats going to need some serious power. 3 screens is roughly 3 times the GPU power required. 120hz means you need 120fps.
120fps x 3 = 360fps required on single screen to achieve 120hz Eyefinity.
I don't think theres any current games you can run at 360fps on anything near decent settings with any of todays hardware. 2 x of the top next gen cards might do it lol.
Of course, anything over 60fps is an increase over standard 60hz screen when using a 120hz screen, but personally i don't think it makes noticable difference until you get 100fps+. So your still looking at needing 300fps on single screen to achieve worthwhile framerates. Anything less than that and you might aswell save a lot of money and get 3 x 60hz screen.
Having a 120hz screen myself I have had musings of a 3 screen setup and the way I would probably do it would be;
Single 120hz screen in the centre for fast multiplayer gaming (where 120hz really shines).
Single 120hz screen in the centre + 2 x 60hz screens on either side for single player gaming in 60hz Eyefinity / Surround on all screens.
Single 120hz screen in the centre for single player gaming in 3D on games that work well with 3D.