Two-dimensional infrared spectroscopy of vibrational probes at an electrode surface shows promise for studying the structural dynamics at an active electrochemical interface. This interface is a complex environment where the solution structures in response to the applied potential. A strategy for achieving the necessary monolayer sensitivity is to use a plasmonically active electrode, which enhances the electromagnetic fields that produce the spectroscopic response. Here, we show how the coupling between the plasmon and the vibrations of the molecular monolayer impacts the FTIR and 2D IR spectroscopy, with an emphasis on the electrochemical potential difference spectra. We show how mixing between the vibrational and plasmonic states gives rise to the distortions that are observed in these measurements. This provides an important step toward 2D IR measurements of vibrational probes at the electrochemical interface as a tool for probing the structural dynamics in the double layer.