FISA is a one man law
In a nutshell, this idea of unitary executive means that everyone in the executive branch--the people whose job it is to enforce the laws and regulations of the United States--must enforce those rules according to the president's wishes. In other words, Bush and Alito and Gonzales and the rest believe that the president is the executive branch and, whether or not he can change the law, can change how laws are enforced.
The question, though, is this: For whom but the president could the law requiring warrants to wiretap American citizens be designed, especially if you believe that the president is the executive branch. Wouldn't that mean that the law is saying, "Mr. President, the people in your charge must get warrants before tapping the phones of American citizens?" If you believe in the "unitary executive," then you have to believe that the law isn't just a blanket statement for law enforcement, but a direct statement to the president which limits his actions.
If you believe in the "unitary executive" and you don't see the law this way, then the only possibility left is that the president simply cannot be restrained by law.