We discuss observations of the quiescent emission from the soft gamma repeater SGR 1806-20 by the Rossi X-ray Timing Explorer. We find that the 2-20 keV RXTE data is consistent with a constant spectral shape during both active bursting periods and periods of relative quiescence, and is best described by a nonthermal (power law) spectral shape. Using archival ASCA data we find that the quiescent spectrum of SGR 1806-20 is well fit over the energy range 1-30 keV by a power law of photon index 2.31 +/- 0.04, with thermal bremsstrahlung and Raymond-Smith models producing much worse fits to the data.