  If the gamma-ray excess from the galactic center reported by Fermi-LAT is a
signal from annihilating dark matter, one must question why a similar excess
has not been observed in dwarf spheroidal galaxies. We use this observation to
place constraints on the density profile of dwarf spheroidal galaxies under the
assumption that the galactic center excess is in fact a signal from
annihilating dark matter. We place constraints on the generalized NFW parameter
$\gamma$ and the Einasto profile parameter $\alpha$ which control the
logarithmic slope of the inner regions of the halo's density profile. We
determine that under these assumptions the galactic center excess is
inconsistent with the standard NFW profile (and other `cuspy' profiles) for
dwarf spheroidal galaxies , but is consistent with observations of cored dwarf
galaxy profiles. Specifically, we find that dwarf spheroidal profiles must be
less cuspy than that of the Milky Way. Models of dark matter which
self-interacts through a light mediator can achieve this.
