  Recent kinematical constraints on the internal densities of the Milky Way's
dwarf satellites have revealed a discrepancy with the subhalo populations of
simulated Galaxy-scale halos in the standard CDM model of hierarchical
structure formation. This has been dubbed the "too big to fail" problem, with
reference to the improbability of large and invisible companions existing in
the Galactic environment. In this paper, we argue that both the Milky Way
observations and simulated subhalos are consistent with the predictions of the
standard model for structure formation. Specifically, we show that there is
significant variation in the properties of subhalos among distinct host halos
of fixed mass and suggest that this can reasonably account for the deficit of
dense satellites in the Milky Way. We exploit well-tested analytic techniques
to predict the properties in a large sample of distinct host halos with a
variety of masses spanning the range expected of the Galactic halo. The
analytic model produces subhalo populations consistent with both Via Lactea II
and Aquarius, and our results suggest that natural variation in subhalo
properties suffices to explain the discrepancy between Milky Way satellite
kinematics and these numerical simulations. At least ~10% of Milky Way-sized
halos host subhalo populations for which there is no "too big to fail" problem,
even when the host halo mass is as large as M_host = 10^12.2 h^-1 M_sun.
Follow-up studies consisting of high-resolution simulations of a large number
of Milky Way-sized hosts are necessary to confirm our predictions. In the
absence of such efforts, the "too big to fail" problem does not appear to be a
significant challenge to the standard model of hierarchical formation.
[abridged]
