  Deep mid-infrared (MIR) observations could reveal a population of faint,
high-redshift (z>3) dusty starburst galaxies that are the progenitors of
present-day spheroids or bulges, and are beyond the reach of current
instruments. We utilize a semi-analytic galaxy formation scheme to find an
extreme model for the MIR galaxy counts, designed to maximize the number of
detectable sources down to a flux level of a few nJy. The model incorporates
the formation of heavily dust-enshrouded stellar populations at high redshift,
and is consistent with existing observations, including faint counts at 1.6um
in the NICMOS Hubble Deep Field, and the upper limit on the extragalactic MIR
background from TeV gamma rays. Our models predict upto 0.5 galaxies/sq.arcsec
at the threshold of 100 nJy at 6um, with a comparable or larger surface density
at longer MIR wavelengths. We conclude that a significant new population of
high-redshift galaxies could be detected by the Space Infrared Telescope
Facility (SIRTF) and Next Generation Space Telescope (NGST). Such a population
would constitute background noise for the Terrestrial Planet Finder (TPF), and
could necessitate repeat observations: every {\it TPF} resolution element have
a 10 percent chance of being contaminated by a background galaxy.
