We present an analysis of NICMOS photometry and low-resolution grism spectroscopy of low-mass stars and sub-stellar objects in the young star-forming region NGC 1333. Our goal is to constrain the ratio of low-mass stars to sub- stellar objects down to 20 Mjup in the cluster as well as constrain the cluster IMF down to 30 Mjup in combination with a previous survey of NGC 1333 by Wilking et al. Our survey covers 4 fields of 51.2 x 51.2, centered on brown dwarf candidates previously identified in Wilking et al. We extend previous work based on the use of a water vapor index for spectral typing to wavelengths accessible with NICMOS on the HST. Spectral types were derived for the 14 brightest objects in our fields, ranging from <M0 - M8, which at the age of the cluster (0.3 Myr) corresponds to a range in mass of >0.25 - 0.02 Msun. In addition to the spectra, we present an analysis of the color-magnitude diagram using pre-main sequence evolutionary models of DAntona & Mazzitelli. Using an extinction-limited sample, we derive the ratio of low-mass stars to brown dwarfs. Comparisons of the observed ratio to that expected from the field IMF of Chabrier indicate that the two results are consistent. We combine our data with that of Wilking et al. to compute the ratio of intermediate-mass stars (0.1 - 1.0 Msun) to low-mass objects (0.03 - 0.1 Msun) in the cluster. We also report the discovery of a faint companion to the previously confirmed brown dwarf ASR 28, as well as a possible outflow surrounding ASR 16. If the faint companion is confirmed as a cluster member, it would have a mass of ~ 5 Mjup (mass ratio 0.15) at a projected distance of 350 AU, similar to 2MASS 1207-3923 B.
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