High-resolution spectra of the Spitzer Space Telescope show vibration-rotation absorption bands of gaseous C2H2, HCN, and CO2 molecules toward a sample of deeply obscured ( U) LIRG nuclei. The observed bands reveal the presence of dense (n greater than or similar to 10(7) cm(-3)), warm (Tex 200-700 K) molecular gas with high column densities of these molecules ranging from a few 1015 to 1017 cm(-2). Abundances relative to H-2, inferred from the silicate optical depth, range from similar to 10(-7) to 10(-6) and show no correlation with temperature. Theoretical studies show that the high abundances of both C2H2 and HCN exclude an X-ray dominated region (XDR) associated with the toroid surrounding an AGN as the origin of this dense warm molecular gas. Galactic massive protostars in the so-called hot-core phase have similar physical characteristics with comparable high abundances of C2H2, HCN, and CO2 in the hot phase. However, the abundances of C2H2 and HCN and the C2H2/CO2 and HCN/CO2 ratios are much higher toward the (U) LIRGs in the cooler ( Tex P 400 K) phase. We suggest that the warm dense molecular gas revealed by the mid-IR absorption lines is associated with a phase of deeply embedded star formation, where the extreme pressures and densities of the nuclear starburst environment have inhibited the expansion of H II regions and the global disruption of the star-forming molecular cloud cores and have "trapped'' the star formation process in an "extended'' hot-core phase.