In any sort of widespread guerrilla-style rebellion (their preferred fantasy, it seems), we would be facing the same problems we faced in Vietnam and Iraq and Afghanistan... what to we bomb?
We dropped more bombs on Vietnam than the world did in WW2. And we lost that one. And we had uninterrupted manufacturing and transportation of war materiel. The Vietnamese were not able to do one damn thing to affect our production of bullets, bombs, rifles, jeeps, APCs, missiles, etc.
Are F-16s going to blow up American bridges and tunnels? Crater American highways and railways? Destroy American power plants and transformer farms? Disable American harbors and airports? Lay waste to entire blocks in American cities and towns? All to try to smoke out guerrillas?
The entire idea is far to complicated to predict what would happen. For example, if there was a general guerrilla rebellion against the federal government, the guerrillas would likely do so much damage to the economy that F-16s would not be able to fly for very long due to a disruption in critical parts to keep them flying. Or to keep their (foreign-made) electronics working.
Of course, the simple solution to your post is "use the AR-15s to kill the people running the surface-to-air missile site, THEN shoot down the F-16". 
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