We demonstrate the generation of a spatiotemporal optical continuum in a highly nonlinear exciton-polariton waveguide using extremely low excitation powers (2-ps, 100-W peak power pulses) and a submillimeter device suitable for integrated optics applications. We observe contributions from several mechanisms over a range of powers and demonstrate that the strong light-matter coupling significantly modifies the physics involved in all of them. The experimental data are well understood in combination with theoretical modeling. The results are applicable to a wide range of systems with linear coupling between nonlinear oscillators and particularly to emerging polariton devices that incorporate materials, such as gallium nitride and transition metal dichalcogenide monolayers that exhibit large light-matter coupling at room temperature. These open the door to low-power experimental studies of spatiotemporal nonlinear optics in submillimeter waveguide devices.