We explore the recently proposed idea that the Galactic dwarf spheroidal galaxies are significantly (by 2 orders of magnitude) more massive than the conventional mass estimates of ${\sim}10^7$ M$_\odot$. In the larger mass case, the observed distribution of stars in these galaxies should have been entirely shaped by internal processes (formation and dynamic relaxation of stars in the potential of the dark matter halo), and not by the Galactic tidal field. We carried out numerical n-body simulations aimed at testing this scenario. Observed properties of three Galactic dwarf spheroidal galaxies were found to be consistent with our model. From our analysis, these dwarfs appear to be massive enough to alleviate the “missing satellites” problem of cold dark matter cosmologies.