Recent determinations of the deuterium abundance, H-2/H, in high redshift Lyman limit hydrogen clouds challenge the usual picture of primordial nucleosynthesis based on ''concordance'' of the calculated light element (H-2, He-3, (4)Ke, Li-7) nucleosynthesis yields with the observationally-inferred abundances of these species. Concordance implies that all light element yields can be made to agree with the observationally-inferred abundances (within errors) for single global specifications of the baryon-to-photon ratio, eta; lepton number; neutron lifetime; and expansion rate (or equivalently, effective number of light neutrino degrees of freedom N-v). Though one group studying Lyman limit systems obtains a high value of H-2/H (similar to 2 x 10(-4)), another group finds consistently low values (similar to 2 x 10(-5)). In the former case, concordance for N-v = 3 is readily attained for the current observationally-inferred abundances of He-4 and Li-7. But if the latter case represents the primordial deuterium abundance, then concordance for any N-v is impossible unless the primordial value of Li-7/H is considerably larger than the abundance of lithium as measured in old, hot Pop II halo stars. Furthermore, concordance with N-v = 3 is possible for low H-2/H only if either (1) the primordial He-4 abundance has been significantly underestimated, or (2) new neutrino sector physics is invoked. We argue that systematic underestimation of both the Li-7 and He-4 primordial abundances is the likely resolution of this problem, a conclusion which is strengthened by new results on He-4.