Obviously the easiest way is to shut off all the utilities, establish a perimeter and just wait it out. How much food and water could they have stockpiled in there anyway?
I can see how that would play out:
1. These 'militiamen' (pfft) will get hungry and will want to leave.
2. Their wives and mommas will show up behind the FBI perimeter with potato bake in hand and crying children in tow, begging for daddy.
3. These 'militiamen' (who are they kidding) will come marching out, guns slung or in-hand but with their children walking alongside them or directly behind them.
4. The FBI, not wanting to risk a firefight with children in the line of fire, will yield and these cunts will walk out.
5. The FBI will later arrest a few ringleaders, but most will get off scot-free.
6. The entire country will apply palm to face.
But more likely, no perimeter will ever be set up, and these rednecks will stay for as long as they please. They may even do a rotating roster, where each wingnut goes only stays a few weeks at a time, like some sort of wacky holiday ranch.