Reionizing the Universe with galaxies appears to require significant star formation in low-mass halos at early times, while local dwarf galaxy counts tell us that star formation has been minimal in small halos around us today. Using simple models and the ELVIS simulation suite, we show that reionization scenarios requiring appreciable star formation in halos with $M_{rm vir} approx 10^{8},M_{odot}$ at $z=8$ are in serious tension with galaxy counts in the Local Group. This tension originates from the seemingly inescapable conclusion that 30 - 60 halos with $M_{rm vir} > 10^{8},M_{odot}$ at $z=8$ will survive to be distinct bound satellites of the Milky Way at $z = 0$. Reionization models requiring star formation in such halos will produce dozens of bound galaxies in the Milky Ways virial volume today (and 100 - 200 throughout the Local Group), each with $gtrsim 10^{5},M_{odot}$ of old stars ($gtrsim 13$ Gyr). This exceeds the stellar mass function of classical Milky Way satellites today, even without allowing for the (significant) post-reionization star formation observed in these galaxies. One possible implication of these findings is that star formation became sharply inefficient in halos smaller than $sim 10^9 ,M_{odot}$ at early times, implying that the high-$z$ luminosity function must break at magnitudes brighter than is often assumed (at ${rm M_{UV}} approx -14$). Our results suggest that JWST (and possibly even HST with the Frontier Fields) may realistically detect the faintest galaxies that drive reionization. It remains to be seen how these results can be reconciled with the most sophisticated simulations of early galaxy formation at present, which predict substantial star formation in $M_{rm vir} sim 10^8 , M_{odot}$ halos during the epoch of reionization.
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