We study the observed cosmic ionizing background as a constraint on the nature of the sources responsible for the reionization of the Universe. In earlier work, we showed that extrapolations of the Ultra-Violet Luminosity Function (LF) of Lyman Break Galaxies (LBGs) at fixed Lyman continuum photon escape fraction are not able to reproduce the redshift evolution of this background. Here, we employ extrapolations of the high-z LFs to describe the contribution of LBGs to the ionizing photon rate, taking into account the smoothing of the baryonic perturbations, due to the background itself (i.e. the filtering mass), as well as a possible sharp increase of the escape fraction in dwarf galaxies. Under the hypothesis of a dominant contribution of LBGs to cosmic reionization, our results suggest that sources fainter than the current observational limits should be characterised by escape fractions of the order of ~0.1-0.3 (larger than the current estimates for bright galaxies) to account for a z>6 reionization and the measured evolution of cosmic ionizing background, at the same time. The contribution to the background from quasars turns out to be relevant at z