Kinematic surveys of the dwarf spheroidal ( dSph ) satellites of the Milky Way are revealing tantalising hints about the structure of dark matter ( DM ) haloes at the low-mass end of the galaxy luminosity function . At the bright end , modelling of spiral galaxies has shown that their rotation curves are consistent with the hypothesis of a Universal Rotation Curve whose shape is supported by a cored dark matter halo . In this paper , we investigate whether the internal kinematics of the Milky Way dSphs are consistent with the particular cored DM distributions which reproduce the properties of spiral galaxies . Although the DM densities in dSphs are typically almost two orders of magnitude higher than those found in ( larger ) disk systems , we find consistency between dSph kinematics and Burkert DM haloes whose core radii r _ { 0 } and central densities \rho _ { 0 } lie on the extrapolation of the scaling law seen in spiral galaxies : \log \ > \rho _ { 0 } \simeq \alpha \ > \log \ > r _ { 0 } + const with 0.9 < \alpha < 1.1 . We similarly find that the dSph data are consistent with the relation between \rho _ { 0 } and baryon scale length seen in spiral galaxies . While the origin of these scaling relations is unclear , the finding that a single DM halo profile is consistent with kinematic data in galaxies of widely varying size , luminosity and Hubble Type is important for our understanding of observed galaxies and must be accounted for in models of galaxy formation .