Yes, the president does have the authority to use military force against American citizens on US soil—but only in "an extraordinary circumstance," Attorney General Eric Holder said in a letter to Sen. Rand Paul (R-Ky.) on Tuesday.Well, nobody doubted that, if "extraordinary" means "a state of war or insurrection." The examples given in the letter are Pearl Harbor and 9/11, both odd examples since they don't involve US citizens as aggressors. If you'd shot down the planes on 9/11, for example, you'd have killed some US citizens... but it would have been accidental to your purpose. It would have been justifiable under the Just War Doctrine of Double Effect for that reason.
I would have thought an example such as the Whiskey Rebellion or the Civil War would have been more to the point. The question isn't whether there might possibly be circumstances in which a President can use military force on US citizens, but exactly what the defining terms are.