Not offering any recommendation, just something based off my own experience. I had built my rig mainly for dual HD7970, and I had picked the LGA2011 platform for my build. With OCing in mind and having a 3960X + 2x HD7970, the Corsair HX1050 was the logical choice. It performed admirably, allowing me to hit 4.7ghz on my CPU, and 1100/1450 on my GPUs, it hardly broke a sweat actually. So, a HX1050 for 2xGTX680's should not be a problem at all, the PSU would hardly break a sweat. Now, why am I so certain? Simple, the HX1050 even handled 3x HD7970 when I upped my GPU's with a third card. It ran my system stably, but I would be first to admit that I was pretty antsy about it. The fact that the air vented from the PSU was a fair bit warmer than with two cards served to only exascerbate matters.
Although the HX1050 seemed to be handling the three cards well enough, I couldn't shake this nagging doubt. After a couple of weeks or so, I decided to put the matter to rest by swapping out the HX1050 with a Seasonic X-1250. After that, I was able to sleep well without worrying about my PSU crapping on me whenever I powered up my main rig.
As for OP, that 650W PSU is cutting it pretty close, and since you can afford an expensive card like the GTX680, why cheap out on PSU? Look at me, I buy the best I can afford, and I never go cheap on the most important component in a system.....the PSU. My HX1050 is not being idle either, I swapped my Seasonic SS-850AT Bronze PSU with it, it is now powering my 2nd rig in my sig. The SS-850AT is now my backup PSU.....