Using data from the Sloan Digital Sky Survey (SDSS; data release 7), we have conducted a search for local analogs to the extremely compact, massive, quiescent galaxies that have been identified at z > 2. We show that incompleteness is a concern for such compact galaxies, particularly for low redshifts (z < ~0.05) as a result of the SDSS spectroscopic target selection algorithm. We have identified 63 massive red sequence galaxies at 0.066 < z < 0.12 that are smaller than the median size-mass relation by a factor of 2 or more. Consistent with expectations from the virial theorem, the median offset from the mass-velocity dispersion relation for these galaxies is 0.12 dex. We do not find any galaxies with sizes and masses comparable to those observed at z ~ 2, implying a decrease in the comoving number density (at fixed size and mass) by a factor of > 5000. This result cannot be explained by incompleteness: at 0.066 < z <0.12, the SDSS spectroscopic sample should typically be ~75% complete for galaxies with the sizes and masses seen at high redshift, although for the very smallest galaxies it may be as low as ~20%. To confirm that the absence of such compact massive galaxies in SDSS is not a spectroscopic selection effect, we have also looked for such galaxies in the SDSS photometric catalog, using photometric redshifts. While we do find signs of a bias against massive, compact galaxies, this analysis suggests that the SDSS spectroscopic sample is missing at most a few objects in the regime we consider. Accepting the high redshift results, it is clear that massive galaxies must undergo significant structural evolution over z<2 in order to match the population seen in the local universe. Our results suggest that a highly stochastic mechanism like major mergers cannot be the primary driver of this strong size evolution.
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