This sounds like a great idea for a low budget film with huge commercial potential if made from the perspective of the officer from with in the silo.

The logline has almost everything it needs, I would say though, in the wrong order and with to many descriptions that don’t push the stakes and personal conflict to the max.

My try:
When an alien force attacks earth a disillusioned officer in control of the last nuclear silo must destroy the invading forces Generals in their newly established head quarters set up in Washington DC in order to save mankind.

Hope this helps.

I think that with this premise it is not about making it believable rather plausible. Pineapple Express was far from believable but was perfectly plausible and its that connection to plausibility that made it’s naturalistic performances funny and the premise fun.

Otherwise the story goes into farce territory, which is fine, but from the sounds of the logline this was not the intention.
However if farce is the idea, then any structure will do really. Chich and Chong building a car out of hemp to smuggle it into the US from Mexico was pretty much a farce that found it’s own audience many years ago this could perhaps work now days as well.

I for one prefer a comedy that is hilarious because it is in touch with reality. The beauty of well crafted comedy is that it provides grounds to critique real life and allows us to say things that we other wise can’t.