We use high resolution N-body/gasdynamical simulations to investigate the effects of a photoionizing UV background on the assembly of disk galaxies in hierarchically clustering universes. We focus on the mass and rotational properties of gas that can cool to form centrifugally supported disks in dark matter halos of different mass. Photoheating can significantly reduce the amount of gas that can cool in galactic halos. Depending on the strength of the UV background field, the amount of cooled gas can be reduced by up to $50\%$ in systems with circular speeds in the range $80$-$200$ \kms. The magnitude of the effect, however, is not enough to solve the ``overcooling'' problem that plagues hierarchical models of galaxy formation if the UV background is chosen to be consistent with estimates based on recent observations of QSO absorption systems. Photoionization has little effect on the collapse of gas at high redshift and affects preferentially gas that is accreted at late times. Since disks form inside-out, accreting higher angular momentum gas at later times, disks formed in the presence of a UV background have spins that are even smaller than those formed in simulations that do not include the effects of photoionization. This exacerbates the angular momentum problem that afflicts hierarchical models of disk formation. We conclude that photoionization cannot provide the heating mechanism required to reconcile hierarchically clustering models with observations. Energy feedback and enrichment processes from the formation and evolution of stars must therefore be indispensable ingredients for any successful model of the formation of disk galaxies.