We present infrared images and spectra of comets 2P/Encke, 67P/Churyumov-Gerasimenko, and C/2001 HT50 (LINEAR-NEAT) as part of a larger program to observe comets inside of 5 AU from the Sun with the Spitzer Space Telescope. The nucleus of comet 2P/Encke was observed at two vastly different phase angles (20° and 63°). Model fits to the spectral energy distributions of the nucleus suggest that comet Encke's infrared beaming parameter derived from the near-Earth asteroid thermal model may have a phase angle dependence. The observed emission from comet Encke's dust coma is best modeled using predominately amorphous carbon grains with a grain size distribution that peaks near 0.4 μm, and the silicate contribution by mass to the submicron dust coma is constrained to <31%. Comet 67P/Churyumov-Gerasimenko was observed with distinct coma emission in excess of a model nucleus at a heliocentric distance of 5.0 AU. The coma detection suggests that sublimation processes are still active or grains from recent activity remain near the nucleus. Comet C/2001 HT50 (LINEAR-NEAT) showed evidence for crystalline silicates in the spectrum obtained at 3.2 AU, and we derive a silicate-to-carbon dust ratio of 0.6. The ratio is an order of magnitude lower than that derived for comets 9P/Tempel 1 during the Deep Impact encounter and C/1995 O1 (Hale-Bopp).