I thought I made that pretty clear. Immediate means 'right this very second'.
Using the example given, if a sniper is killing people from a bell tower, that IS an immediate need.
Using your example, that is a deliberative process. People gather and discuss whether or not to use a drone, how to use it, and who will be the target. To come to the decision to target an American, (whether or not he is abroad or on our soil) is a deliberative process. That means that the government is limited in its actions and must meet certain steps prior to just killing an American.
I am not saying that they can't in a time of war, but I AM saying that they have to follow the rules, and those rules are set forth by the Constitution.
The President is, as usual, dead wrong.