We have searched 92 unidentified sources from the Faint Images of the Radio Sky at Twenty Centimeters (FIRST) and NRAO VLA Sky Survey (NVSS) 1400 MHz radio survey catalogs for radio pulsations at 610 MHz. The selected radio sources are bright, have no identification with extragalactic objects, are pointlike, and are more than 5% linearly polarized. Our search was sensitive to submillisecond pulsations from pulsars with dispersion measures less than ~500 pc cm-3 in the absence of scattering. We have detected no pulsations from these sources and consider possible effects that might prevent detection. We conclude that, as a population, these sources are unlikely to be pulsars.