The mention of a new organization that would undertake covert action also raises the ugly specter of the CIA's abuses in the 1960s and 1970s. Traditionally, this is the area that has gotten the CIA into the most trouble.
The CIA used to have broader powers to conduct missions to topple governments (with doomed operations like the Bay of Pigs), assassinate foreign targets, and even eavesdrop illegally on Americans. After some of its worst abuses were exposed in the 1970s (along with embarrassing episodes like the CIA's attempt to hire a mobster to assassinate Castro and its failed plot to poison the toothbrush of a Congolese rebel leader), a new, more rigorous oversight regime was put in place, and assassinations were forbidden.
In recent years, the CIA has been authorized to capture—or kill—some of the most high-value terrorist targets, but these orders now require a presidential sign-off.