  We calculate the energy that baryons must inject in cold dark matter (CDM)
haloes in order to remove centrally-divergent DM cusps on scales relevant to
observations of dwarf spheroidal galaxies (dSphs). We estimate that the CDM
haloes often associated with the Milky Way's dSphs (M_vir/M_\odot \sim
10^{9-10}) require \Delta E/erg \sim 10^{53-55} in order to form cores on
scales comparable to the luminous size of these galaxies. While supernova type
II (SNeII) explosions can in principle generate this energy, the actual
contribution is limited by the low star formation efficiency implied by the
abundance of luminous satellites. Considering that CDM's well-known `core/cusp'
and `missing satellite' problems place opposing demands on star formation
efficiencies, existing observational evidences for large cores in the most
luminous dSphs require that CDM models invoke some combination of the
following: (i) efficient (of order unity) coupling of SNeII energy into dark
matter particles, (ii) star formation histories peaking at unexpectedly high
redshifts (z>6), (iii) a top-heavy stellar IMF, and/or (iv) substantial
satellite disruption or other stochastic effects to ease the substructure
abundance constraints. Our models show that the tension between CDM problems on
small scales would increase if cored DM profiles were to be found in fainter
dwarves.
