  Recent LHC results suggest a standard model (SM)-like Higgs boson in the
vicinity of 125 GeV with no clear indications yet of physics beyond the SM. At
the same time, the SM is incomplete, since additional dynamics are required to
accommodate cosmological dark matter (DM). In this paper we show that
interactions between weak scale DM and the Higgs which are strong enough to
yield a thermal relic abundance consistent with observation can easily
destabilize the electroweak vacuum or drive the theory into a non-perturbative
regime at a low scale. As a consequence, new physics--beyond the DM
itself--must enter at a cutoff well below the Planck scale and in some cases as
low as O(10 - 1000 TeV), a range relevant to indirect probes of flavor and CP
violation. In addition, this cutoff is correlated with the DM mass and
scattering cross-section in a parameter space which will be probed
experimentally in the near term. Specifically, we consider the SM plus
additional spin 0 or 1/2 states with singlet, triplet, or doublet electroweak
quantum numbers and quartic or Yukawa couplings to the Higgs boson. We derive
explicit expressions for the full two-loop RGEs and one-loop threshold
corrections for these theories.
