I have the ASUS 144hz monitor you are talking about and a GTX 690. I used to have 2 680s, but I switched to a mini-ITX form factor so I needed the extra space.
As for the 144hz monitor, yes you will be able to run most games at 120-144 hz with multiple 680s, not at max settings of course, BUT you have to decide what you want more: 120fps gaming OR max graphics @ around 60fps. For me personally, I do alot of shooter games online like Battlefield 3, so having a 120hz monitor is awesome if you can run the game at the high frame rate.
A word of caution though. Once you go to 120hz+, you will never go back, which is good and bad. It's good because it's so fluid and smooth, and you have a noticeable advantage in online gaming, assuming your PC can run @ 120fps. It's bad because you will want to play all your games at 120fps, which can get more and more expensive, and you will want to upgrade like every 6 months to keep a constant 120fps in your games. Also, after gaming at 120hz for so long, if you try to go back to 60hz, your eyes will start to hurt because your eyes are so used to seeing double the frames for so long. So once you make the move to 120hz+, you will not be able to go back, but if you are like me, then it's worth it.
If you have any other questions about 120hz monitors, shoot me a message, because HHz (high-hertz) gaming is my specialty
