We use absolutely calibrated data between 3 and 90 GHz from the 2006 balloon flight of the ARCADE 2 instrument, along with previous measurements at other frequencies, to constrain models of extragalactic emission. Such emission is a combination of the Cosmic Microwave Background (CMB) monopole, Galactic foreground emission, the integrated contribution of radio emission from external galaxies, any spectral distortions present in the CMB, and any other extragalactic source. After removal of estimates of foreground emission from our own Galaxy, and the estimated contribution of external galaxies, we present fits to a combination of the flat-spectrum CMB and potential spectral distortions in the CMB. We find 2 sigma upper limits to CMB spectral distortions of mu < 5.8 x 10^{-5} and Y_ff < 6.2 x 10^{-5}. We also find a significant detection of a residual signal beyond that which can be explained by the CMB plus the integrated radio emission from galaxies estimated from existing surveys. After subtraction of an estimate of the contribution of discrete radio sources, this unexplained signal is consistent with extragalactic emission in the form of a power law with amplitude 1.06 pm 0.11 K at 1 GHz and a spectral index of -2.56 pm 0.04.
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