If the 680 has two 6-pin connectors itself, you will be fine since the Mac Pro can power a card with two 6-pins safely.
If the 680 is a 6-pin and 8-pin card (which will require you to use a 6 to 8-pin adapter), you will be exceeding the Mac Pro specification and *may* damage the computer in long-term use.
If the 680 is an overclocked 2x 8-pin then you would be highly likely to damage the Mac Pro very quickly. At best you would get unexpected shut downs. At worse you would ruin your logic board.
This topic has been discussed extensively and you will find a lot of information if you search.
There are some good 2x 6-pin 680s such as the MSI 680 4Gb Twin Frozr card if you want one or you could buy a modified 780 from MacVidCards on eBay.