Seth Mason confirms that the question is being asked:
I want to preface this article with an analogy. Owning a fire extinguisher doesn't mean that you plan on your house burning. It simply means that you are prepared in case you have a house fire. In the same way, the question "would you shoot American citizens?" that some troops are supposedly being asked doesn't mean that the Department of Defense is planning to attack American citizens. Furthermore, the question likely has nothing to do with the American people as a whole. It's most likely in reference to U.S. citizens who allegedly have ties to Islamic terrorism. Still, it's a hell of a question, and it goes to show how badly our constitutional rights have been eroded in the name of the War on Terror.
On to the question itself: I have a good friend in-the-know with the military who told me that some troops are being asked if they would shoot American citizens if ordered. If the troops reply that they would not, they are immediately honorably discharged on other grounds, says my friend. This supports Internet rumors about the existence of such of question. I trust my friend, and now I, too, believe that the question is being posed within our military.