El Niño Southern Oscillation (ENSO) exerts a remote impact on the North Pacific and North American winter climate. Both observational and model studies have suggested nonlinearities in this teleconnection. However, it remains unclear if possible nonlinearities arise from the forcing strength or the forcing location in the tropical Pacific, or from factors external to the tropical Pacific. To separate these factors, an idealized model is forced with seasonally varying sea surface temperature with linearly varying strength at a fixed location. Whereas for moderate events the North Pacific response is more linear, strong events exhibit significant nonlinearity both in terms of the strength and location of the impact. The nonlinearity can be traced back to the relationship between sea surface temperature and tropical convection. Nonlinearity in the North Pacific response can have important impacts for long-range prediction and for potential changes in the diversity of ENSO with climate change.