Liquid-phase negative differential resistance (NDR) is observed in the i-V behavior of a conical nanopore (~300 nm orifice radius) in a glass membrane that separates an external low-conductivity 5 mM KCl solution of dimethylsulfoxide (DMSO)/water (v/v 3:1) from an internal high-conductivity 5 mM KCl aqueous solution. NDR appears in the i-V curve of the negatively charged nanopore as the voltage-dependent electro-osmotic force opposes an externally applied pressure force, continuously moving the location of the interfacial zone between the two miscible solutions to a position just inside the nanopore orifice. An ~80% decrease in the ionic current occurs over less that a ~10 mV increase in applied voltage. The NDR turn-on voltage was found to be tunable over a ~1 V window by adjusting the applied external pressure from 0 to 50 mmHg. Finite-element simulations based on solution of Navier-Stokes, Poisson, and convective Nernst-Planck equations for mixed solvent electrolytes within a negatively charged nanopore yield predictions of the NDR behavior that are in qualitative agreement with the experimental observations. Applications in chemical sensing of a tunable, solution-based electrical switch based on the NDR effect are discussed.