Coupling between electromagnetic cavity fields and fluorescent molecules or quantum emitters can be strongly enhanced by reducing the cavity mode volume. Plasmonic structures allow light confinement down to volumes that are only a few cubic nanometers. At such length scales, nonlocal and quantum tunneling effects are expected to influence the emitter interaction with the surface plasmon modes, which unavoidably requires going beyond classical models to accurately describe the electron response at the metal surface. In this context, the quantum hydrodynamic theory (QHT) has emerged as an efficient tool to probe nonlocal and quantum effects in metallic nanostructures. Here, we apply state-of-the-art QHT to investigate the quantum effects on strong coupling of a dipole emitter placed at nanometer distances from metallic particles. A comparison with conventional local response approximation (LRA) and …