As part of an ongoing program to better understand the early stages of massive star cluster evolution and the physical conditions for their formation, we have obtained J, H, K', and N (10.8 μm) images of the nuclear region of the starburst galaxy He 2-10. The N-band images were obtained with the Gemini North Telescope. In only 10 minutes of on-source integration time with Gemini, we were able to detect four of the five enshrouded clusters, or ultradense H II (UD H II regions) recently discovered in radio maps. None of these sources appears in either the optical Hubble Space Telescope images or the near-infrared (J, H, and K') images. These sources make up about 60% of the total N-band flux from He 2-10 and, we suspect, a similar fraction of the total far-infrared flux measured by IRAS. The inferred spectra of the UD H II regions are strikingly similar to those of Galactic ultracompact H II regions. We have modeled the radio and IR spectra of these UD H II regions under the assumption that they are scaled-up Galactic ultracompact H II regions. From this model, the bolometric luminosity of the brightest cluster alone is estimated to be ~2 × 109 L☉. The total mass of the dust and gas in this UD H II region is Mshell ≈ 107 M☉. We have also used the observed spectra to place constraints on the masses and ages of the stellar clusters enshrouded within the UD H II regions. For the brightest UD H II region, we find that the stellar mass must be Mcluster 2.5 × 106 M☉, and the age must be 4.8 × 106 yr, with the most probable age being 3.6 × 106 yr. If we assume that the region is pressure confined and enforce the requirement that the star formation efficiency must be less than ~90%, we find that the age of this stellar cluster must lie within a very narrow range, 4 × 105 < τ < 5 × 106 yr. All the clusters within the UD H II regions in He 2-10 are estimated to have ages less than about 5 × 106 yr and masses greater than about 5 × 105 M☉. We find that the logarithmic ratio of the radio to far-infrared flux densities, q, for the UD H II regions in He 2-10 is ~4; q ≈ 2.6 for both He 2-10 as a whole and NGC 5253, another nearby starburst known to host UD H II regions. These values of q are significantly larger than the average q = 2.35 found for normal galaxies but are comparable to the values of q found for ultraluminous infrared galaxies. We suggest that large q values for starburst galaxies may indicate that a significant fraction of the far-infrared flux may arise from thermal dust emission from UD H II regions. Finally, the possibility that all the far-infrared flux from He 2-10 and other starburst galaxies may be produced by regions completely obscured at wavelengths as long as K' suggests that the well-known correlation between ultraviolet continuum slope and infrared-to-ultraviolet flux ratio in starbursts cannot be due entirely to reprocessing of ultraviolet radiation by dust in a foreground screen geometry. In fact, the dust that reddens the ultraviolet continuum slope must be largely decoupled from the dust that produces the large infrared fluxes in some starbursts.