Here's the weird thing about that gut feeling -- do you really need tens of thousands of combat troops to manage a couple hundred VIP "prisoners"? Pretty sure a single 20-something soldier with a rifle can manage at least a couple 70 year old congressmen.
I do think there's a "keep them in" aspect to all this, but I bet its for more than that. At minimum, optics to send some sort of message. At maximum, defense of a "prison" from an organized group that would seek to break them out.
The number of troops required is based on the area being controlled and the manner of control. Simplest math is 2 man vs 5 man team times intersections controlled (x3 shifts plus cooks and clerks). Adds up quick in an area the size of DC.
I saw how many it took for Baquba in '10. 2500 is about right for that kind of coverage.
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