Recent experiments with metallic nanowires devices seem to indicate that superconductivity can be controlled by the application of electric fields. In such experiments, critical currents are tuned and eventually suppressed by relatively small voltages applied to nearby gate electrodes, at odds with current understanding of electrostatic screening in metals. We investigate the impact of gate voltages on superconductivity in similar metal nanowires. Varying materials and device geometries, we study the physical mechanism behind the quench of superconductivity. We demonstrate that the transition from superconducting to resistive state can be understood in detail by tunneling of high-energy electrons from the gate contact to the nanowire, resulting in quasiparticle generation and, at sufficiently large currents, heating. Onset of critical current suppression occurs below gate currents of 100fA, which are challenging to detect in typical experiments.