This paper demonstrates that a wide range of driven, overdamped, nonlinear systems can exhibit negative differential resistance, where the equilibrium amplitude of oscillation decreases as the amplitude of the driving force increases. As an example, we examine the response of a parametrically driven bistable electronic circuit to both a dichotomous and a sinusoidal driving force. A general condition is derived for the onset of negative damping in the presence of a large amplitude modulation.