  Recent determination of the Hubble constant via Cepheid-calibrated supernovae
by \citet{riess_2.4_2016} (R16) find $\sim 3\sigma$ tension with inferences
based on cosmic microwave background temperature and polarization measurements
from $Planck$. This tension could be an indication of inadequacies in the
concordance $\Lambda$CDM model. Here we investigate the possibility that the
discrepancy could instead be due to systematic bias or uncertainty in the
Cepheid calibration step of the distance ladder measurement by R16. We consider
variations in total-to-selective extinction of Cepheid flux as a function of
line-of-sight, hidden structure in the period-luminosity relationship, and
potentially different intrinsic color distributions of Cepheids as a function
of host galaxy. Considering all potential sources of error, our final
determination of $H_0 = 73.3 \pm 1.7~{\rm km/s/Mpc}$ (not including systematic
errors from the treatment of geometric distances or Type Ia Supernovae) shows
remarkable robustness and agreement with R16. We conclude systematics from the
modeling of Cepheid photometry, including Cepheid selection criteria, cannot
explain the observed tension between Cepheid-variable and CMB-based inferences
of the Hubble constant. Considering a `model-independent' approach to relating
Cepheids in galaxies with known distances to Cepheids in galaxies hosting a
Type Ia supernova and finding agreement with the R16 result, we conclude no
generalization of the model relating anchor and host Cepheid magnitude
measurements can introduce significant bias in the $H_0$ inference.
