MobiusArcher: Its been 3 years since I built my PC, so things may have changed, but power supplies are tricky. You cant go by just wattage. Each power supply will have a bunch of stuff listed on it besides to total wattage, and that stuff is important. On top of that, quality is really important in a PSU.
Aside from wattage the other important thing to check on PSUs is the amps on the +12V rail, as this determines how much power the PSU can actually deliver to the GPU. For most cases if the PSU has the recommended overall wattage then it will also have sufficient amps on the 12V rail, but when dealing with power hungry GPUs its still good to double-check just to be sure. Quality is definitely important, though, since aside from outright failure (usually due to a capacitor blowing) you can have lower quality PSUs not actually delivering the rated power, or not providing a clean stream of power (e.g. voltage dips and spikes), which can cause all kinds of weird behavior.
MobiusArcher: When I was taught to build my own computers I was told there are two components you cant cheap out on. One was the motherboard, the other was the Power supply.
I'd just like to say that whoever taught you taught you well.
As for the OP, it depends on the specific model of PSU that you have. As another poster mentioned, Thermaltake has several different 600W PSUs available; some of them would probably be alright, while others would be more likely to cause problems. For instance, in addition to the 600W requirement, the GTX 770 requires 42 amps on the +12V rail; some of the Thermaltake 600W PSUs (barely) meet this requirement, while others fall just short of it.