The dynamics of the dwarf-spheroidal (dSph) galaxies in the gravitational field of the Galaxy is investigated with particular reference to their susceptibility to tidal break-up. Based on the observed paucity of the dSphs at small Galactocentric distances, we put forward the hypothesis that subsequent to the formation of the Milky Way and its satellites, those dSphs that had orbits with small perigalacticons were tidally disrupted, leaving behind a population that now has a relatively larger value of its average perigalacticon to apogalacticon ratio and consequently a larger value of its r.m.s. transverse to radial velocities ratio compared to their values at the time of formation of the dSphs. We analyze the implications of this hypothesis for the phase space distribution of the dSphs and that of the dark matter (DM) halo of the Galaxy within the context of a self-consistent model in which the functional form of the phase space distribution of DM particles follows the King model, i.e. the 'lowered isothermal' distribution and the potential of the Galaxy is determined self-consistently by including the gravitational cross-coupling between visible matter and DM particles. This analysis, coupled with virial arguments, yields an estimate of J 270 km s ร1 for the circular velocity of any test object at galactocentric distances of $100 kpc, the typical distances of the dSphs. The corresponding self-consistent values of the relevant DM halo model parameters, namely, the local (i.e., the solar neighbourhood) values of the DM density and velocity dispersion in the King model and its truncation radius, are estimated to be $0.3 GeV cm ร3 , >350 km s ร1 and J 150 kpc, respectively. Similar self-consistent studies with other possible forms of the DM distribution function will be useful in assessing the robustness of our estimates of the Galaxy's DM halo parameters.