Nvidia says the recommended PSU is 350 watts. Even with a PSU that supplies less than 350 watts, it could still work. That mostly depends on your other system components. If you're unsure, double check your system wattage by using a PSU calculator.
It depends on the exact PSU model and make. A quality PSU - no issues whatsoever. A crappy model, you will be lucky if it provides more than 150W in practice.