A search for young substellar objects in the {rho} Oph cloud core region has been made with the aid of multiband profile-fitting point-source photometry of the deep-integration Combined Calibration Scan images of the 2MASS extended mission in the J, H, and Ks bands, and Spitzer IRAC images at 3.6, 4.5, 5.8, and 8.0um. The field of view of the combined observations was 1{deg}x9.3', and the 5{sigma} limiting magnitude at J was 20.5. Comparison of the observed spectral energy distributions with the predictions of the COND and DUSTY models, for an assumed age of 1Myr, supports the identification of many of the sources with brown dwarfs and enables the estimation of effective temperature, T_eff_. The cluster members are then readily distinguishable from background stars by their locations on a plot of flux density versus T_eff_. The range of estimated T_eff_ values extends down to ~750K which, based on the COND model, would suggest the presence of objects of sub-Jupiter mass. The results also suggest that the mass function for the {rho} Oph cloud resembles that of the {sigma} Orionis cluster based on a recent study, with both rising steadily toward lower masses. The other main result from our study is the apparent presence of a progressive blueward skew in the distribution of J-H and H-Ks colors, such that the blue end of the range becomes increasingly bluer with increasing magnitude. We suggest that this behavior might be understood in terms of the "ejected stellar embryo" hypothesis, whereby some of the lowest-mass brown dwarfs could escape to locations close to the front edge of the cloud, and thereby be seen with less extinction.