The turbulent kinetic energy (TKE) budget of the surface mixed layer is evaluated at wintertime stations occupied in the vicinity of the strong Gulf Stream (GS) jet. The nonlocal K-profile parameterization (KPP) of vertical fluxes is combined with observed hydrography and meteorology to diagnose TKE production. This KPP-based production is averaged over the surface mixed layer and compared with corresponding averages of observed TKE dissipation rate from microstructure measurements, under assumptions of a homogeneous steady-state balance for the layer-averaged TKE budget. The KPP-based TKE production estimates exceed the mean observed boundary layer dissipation rates at occupied stations by up to an order of magnitude. In cases with strong upper ocean shear, the boundary layer depths predicted by the bulk Richardson number criteria of KPP tend to be deeper than indicated by observed dissipation rates, and thereby including strong entrainment zone shear contributes excessively to the KPP-based diagnosis of TKE production. However, even after correcting this diagnosis of mixed layer depth, the layer-averaged production still exceeds observed dissipation rates. These results have several possible implications, including: (1) KPP tends to overestimate vertical momentum flux in cases with strong shear due to geostrophically balanced thermal wind, unbalanced submesoscale dynamics, or entrainment driven by mixed layer inertial oscillations; (2) a mean local TKE balance does not hold in baroclinic mixed layers due to radiation of inertial waves, divergence in horizontal TKE flux or an inverse cascade to larger scales; and (3) both the boundary layer depth and the remaining TKE budget discrepancies indicate the limited validity of mixed layer models in the simulation of submesoscale ocean phenomena.