Those making the decision had better be damn sure. It's not good enough to have documentation that the American has talked about terrorist acts, or has been in the company of suspected terrorists. We might not like an American citizen who rails against America and claims association with known terrorist groups. It's not enough for some informant to say the American has been plotting terrorist actions.
If there's a enough evidence to try the person for a crime against the nation, then the evidence should be presented to a court before determining further actions. If there's undeniable evidence that the American is planning an attack, then it doesn't take long to run this evidence by a judge in order to decide a course of action -- it can be done quickly.
I can't imagine a situation in which it's best or necessary for the President or a high-level government official to make the decision to kill the American without getting agreement from a judge. I can't understand those who agree that the President or a high-level official should have the power to kill an American citizen without due process. They hide their agreement behind a made-up situation of an American as a high leader in an al Qaeda cell who's actively fighting against Americans -- they then snarkily ask what is supposed to be done, put him to the side while we kill the other bad guys then read him his rights? That's cute, but it's not the issue. In the heat of battle, you'd kill the person and find out his American status later, so the argument is bogus. And even if an unusual situation is presented in which American soldiers are in danger, and it is known that the group presenting the threat contains an American, if the decision to kill the entire group is made, it's understandable that something had to be done quickly. The real issue is when you have the time to follow an American who's suspected of terrorist involvement -- how is this process handled. It requires due process.