Will my 400 W power supply run GTX 660

Solution
450W is a safe assumption as manufacturers need to make sure there is enough for other peripherals.
I really don't think you will have any issues as your system is running low TDP i3 and assuming nothing else in the case.
GTX660 has TDP of 140W, your CPU probably around 65W and rest of components shouldn't use more then say 20W.
As long as your PSU is of good quality and efficiency, you shouldn't have a problem for now.
But if you start upgrading to i5 and and extra HDD's then definitely get a bigger PSU.

Bare in mind i'm running i7 with GTX660 on 450W so output difference in our PSU's is similar to TDP difference in CPU.
450W is a safe assumption as manufacturers need to make sure there is enough for other peripherals.
I really don't think you will have any issues as your system is running low TDP i3 and assuming nothing else in the case.
GTX660 has TDP of 140W, your CPU probably around 65W and rest of components shouldn't use more then say 20W.
As long as your PSU is of good quality and efficiency, you shouldn't have a problem for now.
But if you start upgrading to i5 and and extra HDD's then definitely get a bigger PSU.

Bare in mind i'm running i7 with GTX660 on 450W so output difference in our PSU's is similar to TDP difference in CPU.
 
Solution
Yes it's possible as long as your PSU has the correct Amps to push the card. But I would not dare overclock it and if your CPU and/or RAM is already overclocked, then downclock them and also remove all optical drives besides 1 and you should be ok. If your have a good 400w PSU, it should be ok, but if you have. cheapo no name brand, then definitely upgrade the PSU or opt for a GTX 750 Ti as that card uses much less power and performs at around GTX 660 levels easily and that card will work fine with your current 400w unit.