I do not believe that the president should have the power to order extrajudicial killings. We have division of power within our government for a reason, namely to prevent abuses of power by any one branch. Enabling the president to order killings without judicial process is a recipe for disaster, as it would essentially allow the president to kill anyone who disagrees.
The president should not have the power to order murder outside the legal system. American citizens are guaranteed a certain amount of rights that should never be taken away. The only exception should be in an extreme case of national emergency. Even though, that power should be carefully exercised and should be guarded against.