Can I crossfire two HD6950’s on this motherboard?

Motherboard:Gigabyte P67A-UD3-B3

In the event yes, what PSU would be powerful enough

That board supports Crossfire, certainly; but 16x/4x Crossfire.So I would suggest the use of the upcoming model in place (P67A-UD4-B3) — which in turn supports 8x/8x Crossfire.
http://www.newegg.com/Product/Product.aspxItem=N82E16813128478 Only $5 more than the UD3-B3.

As far a power supply to perform 2x HI-DEF 6950s CF, I’d opt for the Corsair HX 750w:
http://www.newegg.com/Product/Product.aspxItem=N82E16817139010.