We present visible and near-IR spectra of the nucleus of comet 162P/Siding Spring (also known as 2004 TU12) obtained in 2004 December, while it had no detectable coma. This is the third object observed to have intermittent cometary activity even when relatively close to the Sun. The spectra show no strong features in this wavelength range. This paucity of deep absorptions is common among low-albedo asteroids and the few comet nuclei observed in this spectral region. Marginal spectral structure is observed in the visible spectrum, and beyond 2 μm the flux from the nucleus is dominated by thermal emission. We compare the spectrum of 162P with published spectra of other comet nuclei, primitive asteroids, and meteorites. Comet nuclei display a range of spectral shapes and slopes not unlike those observed among outer main-belt asteroids but closest to Trojan asteroids. No suitable spectral matches to comet 162P were found among primitive (chondritic) meteorites. We modeled our visible and near-IR spectra using the scattering theory described by Shkuratov et al. (1999), and our approach is similar to that used by Emery and Brown for modeling Trojan asteroids. Our best fits to the spectral shape and albedo include mixtures containing amorphous carbons, organics, and silicates. The absence of strong spectral features prevents the identification of specific minerals, and the resulting model compositions are not unique. The observations beyond 2 μm are interpreted in a companion publication by Fernández and coworkers.