We present a sample of normal Type Ia supernovae (SNe Ia) from the Nearby Supernova Factory data set with spectrophotometry at sufficiently late phases to estimate the ejected mass using the bolometric light curve. We measure 56Ni masses from the peak bolometric luminosity, then compare the luminosity in the 56Co-decay tail to the expected rate of radioactive energy release from ejecta of a given mass. We infer the ejected mass in a Bayesian context using a semi-analytic model of the ejecta, incorporating constraints from contemporary numerical models as priors on the density structure and distribution of 56Ni throughout the ejecta. We find a strong correlation between ejected mass and light-curve decline rate, and consequently 56Ni mass, with ejected masses in our data ranging from 0.9 to 1.4 M. Most fast-declining (salt2 x 1 < −1) normal SNe Ia have significantly sub-Chandrasekhar ejected masses in our fiducial analysis.