The detection of gamma-rays from dark matter (DM) annihilation is among the scientific goals of the Fermi Large Area Telescope (formerly known as GLAST) and Cherenkov telescopes. In this paper we investigate the existence of realistic chances of such a discovery selecting some nearby dwarf spheroidal galaxies (dSph) as a target. We study the detectability with the Fermi-LAT of the gamma-ray flux from DM annihilation in Draco, Ursa Minor, Carina, and Sextans, for which the state-of-art DM density profiles were available. We assume the DM is made of Weakly Interacting Massive Particles such as the Lightest Supersymmetric Particle (LSP) and compute the expected gamma-ray flux for optimistic choices of the unknown underlying particle physics parameters. We then compute the boost factors due to the presence of DM clumps and of a central supermassive black hole. Finally, we compare our predictions with the Fermi-LAT sensitivity maps. We find that the dSph galaxies shine above the Galactic smooth halo: e.g., the Galactic halo is brighter than the Draco dSph only for angles smaller than 2.3 degrees above the Galactic Center. We also find that the presence of a cusp or a constant density core in the DM mass density profile does not produce any relevant effect in the gamma-ray flux due to the fortunate combination of the geometrical acceptance of the Fermi-LAT detector and the distance of the galaxies and that no significant enhancement is given by the presence of a central black hole or a population of sub-subhalos. We conclude that, even for the most optimistic scenario of particle physics, the gamma-ray flux from DM annihilation in the dSph galaxies of the LG would be too low to be detected with the Fermi-LAT.
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