We have searched 75 unidentified radio sources selected from the NRAO VLA Sky Survey (NVSS) catalog for the presence of rapidly spinning pulsars and short, dispersed radio bursts. The sources are radio bright, have no identifications or optical source coincidences, are more than 5% linearly polarized, and are spatially unresolved in the catalog. If these sources are fast-spinning pulsars (e.g. sub-millisecond pulsars), previous large-scale pulsar surveys may have missed detection due to instrumental and computational limitations, eclipsing effects, or diffractive scintillation. The discovery of a sub-millisecond pulsar would significantly constrain the neutron star equation of state and would have implications for models predicting a rapid slowdown of highly recycled X-ray pulsars to millisecond periods from, e.g., accretion disk decoupling. These same sources were previously searched unsuccessfully for pulsations at 610 MHz with the Lovell Telescope at Jodrell Bank. This new search was conducted at a different epoch with a new 800 MHz backend on the NRAO 43-meter Telescope at a center frequency of 1200 MHz. Our search was sensitive to sub-millisecond pulsars in highly accelerated binary systems and to short transient pulses. No periodic or transient signals were detected from any of the target sources. We conclude that diffractive scintillation, dispersive smearing, and binary acceleration are unlikely to have prevented detection of the large majority of the sources if they are pulsars, though we cannot rule out eclipsing, nulling or intermittent emission, or radio interference as possible factors for some non-detections. Other (speculative) possibilities for what these sources might be include radio-emitting magnetic cataclysmic variables or older pulsars with aligned magnetic and spin axes.
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