Depends on what hardware you have in your system, a 6670 can only use 75w max due to not having an external PCIE connector:
Though, I suggest getting a 7750, it uses the same power and is around the performance of a 6770
My personal opinion on this is, it might work its just a question of how long.
Maybe take a pic of the side of the psu label so we can see how much power it can really output? Most OEM (like dells, gateways, etc power supplies) manufacturers lie on the labels and put down whatever they feel like.