The vast majority of dwarf satellites orbiting the Milky Way and M31 are quenched , while comparable galaxies in the field are gas-rich and star-forming . Assuming that this dichotomy is driven by environmental quenching , we use the ELVIS suite of N -body simulations to constrain the characteristic timescale upon which satellites must quench following infall into the virial volumes of their hosts . The high satellite quenched fraction observed in the Local Group demands an extremely short quenching timescale ( \sim 2 Gyr ) for dwarf satellites in the mass range { M } _ { \star } \sim 10 ^ { 6 } -10 ^ { 8 } ~ { } { M } _ { \odot } . This quenching timescale is significantly shorter than that required to explain the quenched fraction of more massive satellites ( \sim 8 Gyr ) , both in the Local Group and in more massive host halos , suggesting a dramatic change in the dominant satellite quenching mechanism at { M } _ { \star } \lesssim 10 ^ { 8 } ~ { } { M } _ { \odot } . Combining our work with the results of complementary analyses in the literature , we conclude that the suppression of star formation in massive satellites ( { M } _ { \star } \sim 10 ^ { 8 } -10 ^ { 11 } ~ { } { M } _ { \odot } ) is broadly consistent with being driven by starvation , such that the satellite quenching timescale corresponds to the cold gas depletion time . Below a critical stellar mass scale of \sim 10 ^ { 8 } ~ { } { M } _ { \odot } , however , the required quenching times are much shorter than the expected cold gas depletion times . Instead , quenching must act on a timescale comparable to the dynamical time of the host halo . We posit that ram-pressure stripping can naturally explain this behavior , with the critical mass ( of { M } _ { \star } \sim 10 ^ { 8 } ~ { } { M } _ { \odot } ) corresponding to halos with gravitational restoring forces that are too weak to overcome the drag force encountered when moving through an extended , hot circumgalactic medium .