The GTX 680 can run 3 1080p monitors at the same time. However, you will not get excellent framerates out of it. I am currently playing Assassin's Creed 2 in triple monitor with a Zotac GTX 680 (reference). Although it plays out pretty well, there are points where there is definitely some lag. A game like Battlefield 3, which has more graphics power behind it, will require even more power. You might be better off to consider a dual 660 setup; I hear those work very well for a lot of people. Or you might be willing to sacrifice some of the detail, but it's really up to you
EDIT: Also remember that Eyefinity and Surround are equivalent technologies, but one is from AMD and one is from Nvidia. If you want to use a 680, you will be using Nvidia Surround. This is just the software that let's you connect the triple monitors and have the game display properly, though; it does not guarantee you will get consistently good framerates