1. Cut off landline phones in his part of the WH.
2. Shut off cell phone towers in the area.
3. Shut off electricity.
4. Shut off water.
5. Shut off heat.
6. Guard all doors so no one can enter with supplies.
7. Reverse engineer toilets to spew raw sewage.
He'll give up in 1-2 hours max.
Other than #7 and the timeframe, that might be pretty much what might happen*, albeit implemented incrementally. I couldn't imagine the military being used to get him out as others have espoused.
* If he tried to stay on and in the building, which I don't really think will happen. It's just a hypothetical scenario. Probably.
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