  We observed three regions of the sky with Spitzer in which the Cosmic
InfraRed Background (CIRB) has been determined at 3.5 microns using the method
of subtracting 2MASS stellar fluxes from zodiacal light subtracted DIRBE maps.
For each of these regions we have obtained 270 seconds of integration time per
pixel with IRAC on Spitzer over the central square degree. We present galaxy
counts in each of these approximately 1 square degree IRAC surveys. Along with
deep galaxy counts in the Extended Groth Strip and GOODS North, we are able to
compare the galactic contribution to the CIRB with the "DIRBE minus 2MASS''
determined L-band CIRB. Using the profile-fit photometry package GIM2D, we find
a substantially larger flux contribution to the CIRB than that determined using
aperture photometry. We have also made the first rigorous analysis of the
uncertainties in determining the CIRB via galaxy counts in Spitzer images using
a Monte Carlo Markov Chain simulation of our data analysis. Using a simple
broken power law model for galaxy counts as a function of magnitude we find a
most probable contribution to the CIRB from galaxies at 3.6 microns of
10.8^{+2.1}_{-1.1} kJy/sr. Even with this restricted model, however, we find
that galaxy counting does not strongly constrain the CIRB from above. We are
able to find solutions in which the CIRB runs away to large intensities without
the need for an additional diffuse source.
