No administration has ever had the Constitutional authority to kill US citizens on US soil without a trial. Mr. Obama's refusal to respond to Rand Paul's demand for a commitment not to do so leaves the impression that Mr. Obama believes he can use our military to murder American citizens in their homes and on the streets.
This commitment would in no way reduce Mr. Obama's legitimate authority in this area, since he currently has none. He should end the public relations nightmare he is creating for himself by affirming clearly and publicly that the federal government has no such authority and will not seek it.
Anything less is an admission by a man who has already felt compelled to deny that he's a "dictator" or "emperor" that he does not recognize Constitutional limits to his power.