Understanding cosmic reionization requires the identification and characterization of early sources of hydrogen-ionizing photons. The 2012 Hubble Ultra Deep Field (UDF12) campaign has acquired the deepest infrared images with the Wide Field Camera 3 aboard Hubble Space Telescope and, for the first time, systematically explored the galaxy population deep into the era when cosmic microwave background (CMB) data indicates reionization was underway. The UDF12 campaign thus provides the best constraints to date on the abundance, luminosity distribution, and spectral properties of early star-forming galaxies. We synthesize the new UDF12 results with the most recent constraints from CMB observations to infer redshift-dependent ultraviolet (UV) luminosity densities, reionization histories, and electron scattering optical depth evolution consistent with the available data. Under reasonable assumptions about the escape fraction of hydrogen ionizing photons and the intergalactic medium clumping factor, we find that to fully reionize the universe by redshift z~6 the population of star-forming galaxies at redshifts z~7-9 likely must extend in luminosity below the UDF12 limits to absolute UV magnitudes of M_UVsim -13 or fainter. Moreover, low levels of star formation extending to redshifts z~15-25, as suggested by the normal UV colors of zsimeq7-8 galaxies and the smooth decline in abundance with redshift observed by UDF12 to zsimeq10, are additionally likely required to reproduce the optical depth to electron scattering inferred from CMB observations.