This is truly an outrage. Attorney General Eric Holder, in response to a question from Senator Rand Paul, confirms that the Obama administration claims the right to militarily target Americans on US soil:

As members of this administration have previously indicated, the US government has not carried out drone strikes in the United States and has no intention of doing so. As a policy matter moreover, we reject the use of military force where well-established law enforcement authorities in this country provide the best means for incapacitating a terrorist threat. We have a long history of using the criminal justice system to incapacitate individuals located in our country who pose a threat to the United States and its interests abroad. Hundreds of individuals have been arrested and convicted of terrorism-related offenses in our federal courts.

The question you have posed is therefore entirely hypothetical, unlikely to occur, and one we hope no president will ever have to confront. It is possible, I suppose, to imagine an extraordinary circumstance in which it would be necessary and appropriate under the Constitution and applicable laws of the United States for the President to authorize the military to use lethal force within the territory of the United States. For example, the president could conceivably have no choice but to authorize the military to use such force if necessary to protect the homeland in the circumstances like a catastrophic attack like the ones suffered on December 7, 1941, and September 11, 2001.