but the amount of energy that would be required to free it.
From... ice? 2kJ per kg per Kelvin, usually.
Meaning where does all that energy come from?
If the base is outside of the region of permanent shadow, probably the sun. Melting ice is hardly a difficult problem. The rest of fuel production, yeah, energy requirements out the wazzoo. But just melting ice?
Which I think is not related to the question at hand, since it's very unlikely that the U.S. would decide to go beyond a basic outpost on the Moon as a first goal.
If we're talking "likely", NASA/Congress is unlikely to do anything beyond sorties. Flags'n'footprints. Nothing long term, nothing that lasts beyond local sunset. So why discuss anything?
Because you aren't going to have an "outpost", however small, outside of a tiny number of awkward locations at the Sth Pole without a steady night-time power-source like a nuke. And if you have a nuke, the energy problem is solved wherever you are.
Even at those awkward but well-lit polar sites, you still experience a few days in a row of "night" (not as many, not as often, but some), so without a nuke you'll need buckets of solar and plenty of battery storage. Thankfully, modern solar is cheap/light.
Your big issues will therefore be daytime cooling and the amount of fuel required for transport to support the base.
... Why if only there was a nice pile of cold stuff near those sites which you could dump heat into
and it was also stock for producing fuel. Wouldn't that be handy?
[edit: Wouldn't it be even better if that same pile of cold stuff was also of potentially extraordinary scientific importance, and hence the perfect place to locate a science-centric base anyway?]
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