It is feasible that a 550W PSU could power a system with a 580. Depends on the PSU and the Amps available on the 12V rail. You'd need around 35A available at a minimum.
My system with 2 580s peaks right around 660W (drawing 780W from the wall).
That being said, my recommendation would be to run with at least a 650W Corsair, Seasonic, or XFX PSU. These supplies provide sufficient amps on the 12V rail.
What kind of PSU are you working with?