Exciton polaritons based on atomically thin semiconductors are essential building blocks of quantum optoelectronic devices. Their properties are governed by an ultrafast and oscillatory energy transfer between their excitonic and photonic constituents, resulting in the formation of polaritonic quasiparticles with pronounced nonlinearities induced by the excitonic component. In metallic, plasmonic nanoresonators, dissipation phenomena limit the polariton lifetime to a few tens of femtoseconds, so short that the role of these polaritons for the nonlinear response of such hybrids is yet unexplored. Here we use ultrafast two-dimensional electronic spectroscopy (2DES) to uncover coherent polariton dynamics in a hybrid monolayer (1L) WS2/plasmonic nanostructure. With respect to an uncoupled WS2 flake, we observe an over 20-fold, polarization-dependent enhancement of the optical nonlinearity and a rapid evolution of the 2DES spectra within ~70 fs. We relate these dynamics to a transition from coherent polaritons to incoherent excitations, unravel the microscopic origin of the optical nonlinearities and show the potential of coherent polaritons for ultrafast all-optical switching.