We report Si-29 nuclear magnetic resonance measurements in single crystals and aligned powders of URu2Si2 in the hidden order and paramagnetic phases. The spin-lattice relaxation data reveal evidence of pseudospin fluctuations of U moments in the paramagnetic phase. We find evidence for partial suppression of the density of states below 30 K and analyze the data in terms of a two-component spin-fermion model. We propose that this behavior is a realization of a pseudogap between the hidden-order transition T-HO and 30 K. This behavior is then compared to other materials that demonstrate precursor fluctuations in a pseudogap regime above a ground state with long-range order.