We infer the UV luminosities of Local Group galaxies at early cosmic times ($z sim 2$ and $z sim 7$) by combining stellar population synthesis modeling with star formation histories derived from deep color-magnitude diagrams constructed from Hubble Space Telescope (HST) observations. Our analysis provides a basis for understanding high-$z$ galaxies - including those that may be unobservable even with the James Webb Space Telescope (JWST) - in the context of familiar, well-studied objects in the very low-$z$ Universe. We find that, at the epoch of reionization, all Local Group dwarfs were less luminous than the faintest galaxies detectable in deep HST observations of blank fields. We predict that JWST will observe $z sim 7$ progenitors of galaxies similar to the Large Magellanic Cloud today; however, the HST Frontier Fields initiative may already be observing such galaxies, highlighting the power of gravitational lensing. Consensus reionization models require an extrapolation of the observed blank-field luminosity function at $z approx 7$ by at least two orders of magnitude in order to maintain reionization. This scenario requires the progenitors of the Fornax and Sagittarius dwarf spheroidal galaxies to be contributors to the ionizing background at $z sim 7$. Combined with numerical simulations, our results argue for a break in the UV luminosity function from a faint-end slope of $alpha sim -2$ at $M_{rm UV} < -13$ to $alpha sim -1.2$ at lower luminosities. Applied to photometric samples at lower redshifts, our analysis suggests that HST observations in lensing fields at $z sim 2$ are capable of probing galaxies with luminosities comparable to the expected progenitor of Fornax.
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