We present a sample of normal type Ia supernovae from the Nearby Supernova Factory dataset 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 the ejected mass and the light curve decline rate, and consequently the 56Ni mass, with ejected masses in our data ranging from 0.9–1.4 M⊙. Most fast-declining (SALT2 x1 < −1 or ∆m15,B > 1.2) normal SNe Ia have significantly sub-Chandrasekhar ejected masses in our analysis. At least two progenitor scenarios seem to be necessary to explain our observations.