We present visible and near-infrared spectra of the nucleus of comet 28P/Neujmin 1, obtained in 2001, 2002, and 2003, while it had no detectable coma. The spectra show no strong features in this wavelength range, which prevented the identification of specific compounds on the surface of comet 28P. We found evidence for spectral variability, as our 2002 near-infrared spectrum has a significantly steeper slope than those obtained in 2001 and 2003. We compare the spectra of 28P with published spectra of other comet nuclei, with primitive asteroids and with meteorites. At near-infrared wavelengths, all the comet nuclei show spectra with "red" slopes and the 2002 spectrum of comet 28P is among the reddest even when compared with Trojan asteroids. Three of the four properly observed Jupiter-family comets have significantly redder spectral slopes in the near-infrared than the one Halley-type comet in this sample. We found reasonably good matches among Trojan asteroids to the albedo and spectral shape of comet 28P. Such similarities are consistent with an analogous formation and evolutionary environment for Trojan asteroids and Jupiter-family comets, as proposed by Morbidelli and coworkers. One CI meteorite showed a partial fit to our 2003 near-infrared spectrum of comet 28P; however, no close spectral matches to our target were found among chondritic meteorites.