I like playing with the cool calculator on the coolchips website.
I tried to imagine supplying the same power that you could to a reasonable TEC. My thoughts were 3W per W transferred, for an 80W Load.
Then, it would be reasonable to assume you could keep the hot side at 40 degrees C.
This would give you a cold side temp of, wait for it........
-154.89 degrees C
Obviously, you wouldn't beable to insulate this well enough to prevent heat coming from other sources, so the temp would be a bit higher.
Alternatively, -10 cold side from 40 hot side would only require 27W for an 80W heat load.
If I'm not mistaken, that could easily be run off the PSU.
8-ball