NBC News has revealed a 16-page Justice Department memo laying out the conditions under which the government can authorize the killing of a U.S. citizen. Mark Ambinder has a good summary of the memo, which essentially says the person must represent an "imminent threat" of an attack in the United States and must be in a place where capturing them must be infeasible. Spencer Ackerman looks into the increasingly flexible definition of "imminence" here.
Some readers might be confused about why American al Qaeda members such as Anwar al-Awlaki and Samir Khan are still U.S. citizens. You may have noticed text on your passport noting that you "may lose your U.S. citizenship" by "serving in the armed forces of a foreign state." Why isn't joining a terrorist organization and advocating attacks against the United States grounds for losing your citizenship?
In the 1967 case Afroyim v. Rusk, the Supreme Court ruled that under the 14th amendment, U.S. citizens cannot be involuntarily stripped of their citizenship. (That case involved a dual U.S.-Israeli citizen who had his U.S. citizenship revoked after voting in an Israeli election, but the precedent applies to military service as well.)
Since Afroyim, it's been nearly impossible for someone to be involuntarily stripped of U.S. citizenship. Even if you join a foreign army fighting against the United States, the law says you will only lose your citizenship if you do so "with the intention of relinquishing United States nationality." That intention can be tough to prove, and in Awlaki's case, the administration made no effort to do so.
GOP House members have introduced legislation to investigate whether joining a terrorist organization constitutes a renunciation of citizenship. But frankly, given that U.S. citizenship doesn't seem to provide much protection when a drone has you in its sights, I'm not sure there would be any point.