The incompatibility of the properties of the x-ray background (XRB) with AGNs contributing > 60% at energies of a few KeV has often been interpreted as being due to a substantial contribution of a new population of yet unrecognized x-ray sources. The existence of such population has been recently suggested also by an analysis of very deep ROSAT observations (Hasinger et al. 1993) which revealed a considerable excess of faint x-ray sources over that expected from QSO evolution models, and that the average spectrum of the resolved sources becomes harder with decreasing ux limit. These sources could be extragalactic in origin, but if they make a substantial contribution to the XRB then they must exhibit much weaker clustering than galaxies or QSOs in order to be consistent with the stringent constraints on source clustering imposed by autocorrelation analyses of the unresolved XRB.We investigate the possibility that the indicated new population of x-ray sources is Galactic in origin. Examining spherical halo and thick disk distributions, we derive the allowed properties of such population which would resolve the discrepancy found in the number counts of faint sources, and be consistent with observational constraints on the total background intensity, the XRB anisotropy, the number of unidenti ed bright sources, the Galaxy's total x-ray luminosity, and with the results of uctuation analyses of the unresolved XRB.We nd that a attened Galactic halo (or a thick disk) distribution with a scale height of a few Kpc is consistent with all the above requirements. The typical x-ray luminosity of the sources is 10 30 31 erg/s in the 0:5-2 KeV band, the number density of sources in the Solar vicinity is 10 4:5 pc 3 , their total number in the Galaxy is 10 8:5 , and their total contribution to the Galaxy's x-ray luminosity is 10 39 erg/s. We discuss the possible nature of these sources, including them being subdwarfs, LMXBs, and old neutron stars. We argue that the inferred x-ray and optical luminosities of the sources, their 2-4 KeV spectrum, and the derived local number density and spatial distribution are all consistent with them being intrinsicly faint cataclysmic variables with low accretion rates. We suggest a few possibilities for the origin of such population, including an origin from disrupted globular clusters or dark clusters. We make predictions and suggest tests that could either con rm or rule out our proposal in the near future.