  The direct detection of dark matter through its elastic scattering off
nucleons is among the most promising methods for establishing the particle
identity of dark matter. The current bound on the spin-independent scattering
cross section is sigma^SI < 10 zb for dark matter masses m_chi ~ 100 GeV, with
improved sensitivities expected soon. We examine the implications of this
progress for neutralino dark matter. We work in a supersymmetric framework
well-suited to dark matter studies that is simple and transparent, with models
defined in terms of four weak-scale parameters. We first show that robust
constraints on electric dipole moments motivate large sfermion masses mtilde >
1 TeV, effectively decoupling squarks and sleptons from neutralino dark matter
phenomenology. In this case, we find characteristic cross sections in the
narrow range 1 zb < sigma^SI < 40 zb for m_chi > 70 GeV. As sfermion masses are
lowered to near their experimental limit mtilde ~ 400 GeV, the upper and lower
limits of this range are extended, but only by factors of around two, and the
lower limit is not significantly altered by relaxing many particle physics
assumptions, varying the strange quark content of the nucleon, including the
effects of galactic small-scale structure, or assuming other components of dark
matter. Experiments are therefore rapidly entering the heart of dark
matter-favored supersymmetry parameter space. If no signal is seen,
supersymmetric models must contain some level of fine-tuning, and we identify
and analyze several possibilities. Barring large cancellations, however, in a
large and generic class of models, if thermal relic neutralinos are a
significant component of dark matter, experiments will discover them as they
probe down to the zeptobarn scale.
