It had never been legal, sans due process, for the US President to shoot to kill a US Citizen. Nor has it ever been legal to order the same of his underlings. That would deny us our rights — our constitutionally claimed God given rights.
Not many people would deny that Anwar al-Awlaki was a bad guy and deserved to die for the safety of our nation. But that view misses the point. To overlook the legality of denying him his rights, because he was a special case, means that you or I could be a special case someday too. And that is the point. Our rights were given to all citizens for that very reason.
Whether you trust President Obama to use this power wisely or not makes no difference. One president is given power and it passes to every president that follows. When it becomes lawfully acceptable for the person in the most powerful position in the nation to deny the rights of select citizens, with no burden of proof and no need to explain, does that sound like the United States of America to you?