I speculated that the administration might have figured they wanted no more losses and that it could live with losing those on the ground already. That's why we didn't even commit air power:
Then we might have had the information higher ups needed to commit ground forces. We failed here, assuming the worst and cutting our losses--we had our magical "exit strategy" and followed it rather than trying to win--or even trying to find out if we could win. Instead, the decision was made to go to Las Vegas to raise funds for the one battle our president is fully committed to winning--the White House.
This was a small-scale example of the whole "exit strategy" fetish where we establish what we are willing to lose before a war and then retreat when we hit that level of loss.
Ledeen says that is exactly why the administration halted rescue operations by the military:
The big reason is fear of failure, a big public failure. It was easier to live with tragedy and even a perception of indecisiveness-verging-on-cowardice than with an AC130 gunship going down in flames.
The really ugly part is that since non-military reinforcements who did make it in rescued many on the ground, the administration was apparently willing to lose a lot more than four of our men in the incident.