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 $^{56}$Ni masses from the peak bolometric luminosity, then compare the luminosity in the $^{56}$Co-decay tail to the expected rate of radioactive energy re- lease 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 $^{56}$Ni throughout the ejecta. We find a strong correlation between ejected mass and light curve decline rate, and consequently $^{56}$Ni mass, with ejected masses in our data ranging from 0.9-1.4 $M_odot$. Most fast-declining (SALT2 $x_1 < -1$) normal SNe Ia have significantly sub-Chandrasekhar ejected masses in our fiducial analysis.