No, each 680 doesn't need 42 amps under any circumstances. Nvidia states 42 amps minimum for the power supply because it needs to power the whole system. When going with a pair of 680s, you just add about 15 amps. Since that is at 12V, 15 amps makes for 180W. (W=V*A) There's some headroom to overclock on that power supply. In addition, that recommendation is only under the most severe circumstances. Most of the time gaming won't even bring you within 80% of that rating. Some benchmarks might, though.
Mine is only rated for 62A on the 12V rail, and I have no problems with overclocking both my GPUs and my CPU. Under normal gaming, with those all mildly overclocked I still have plenty of headroom on my power supply.
Edit: Apparently, my memory isn't the greatest at accuracy. I remembered them saying during the initial reviews that the GTX680 was 180W, but I looked up the specs and they say 195W. So, each GTX680 uses about 16.3 amps, not 15 as I originally stated. Not a huge difference, but accuracy must be maintained. Even if you overclock it to use the maximum 225W the connectors are speced to deliver, that's still only 18.75 amps. So, add up the two 680s overclocked to 225W levels, 37.5 amps, plus your CPU, memory, motherboard, and drives, and you're still probably under 50 amps on that 12V rail.