We discuss recent models in which neutrinos, which are assumed to have mass in the eV range, originate the highest energy cosmic rays by interaction with the enhanced density in the galactic halo of the relic cosmic neutrino background. We make an analytical calculation of the required neutrino fluxes to show that the parameter space for these models is constrained by horizontal air shower searches and by the total number of background neutrinos, so that only models which have fairly unnatural halo sizes and enhanced densities are allowed.