Well, it really is sort of simple. “To execute” means to carry out. The POTUS is to see that policies and programs are carried out. POTUS is chief cook and bottle washer.
So, what’s the problem? For several reasons (laziness, cowardice, greed) the electoral process has been perverted by the pretense that the executive, not the legislative body, is the source of policy. The unitary executive people want to make the pretense reality because a temporary tyrant is a convenient figurehead for exploiters to hide behind. (Cheney’s former company profiteering from the Iraq invasion is a good example of how it is supposed to work).
If the proponents of the unitary executive seem unclear about what they want, it is likely because they are incompetent people who do not know what “carry out,” “deliver” or “produce” means. During the Iraq debacle, it seemed they took the intent for the act. More recently it seems obvious that they do not even know what action is. Withholding funds is non-action par excellence. At least Obama had the excuse that he believed the federal deficit is an impediment to economic growth. Who knew the Dude would use it for his personal gratification?
Finally, how are the denizens of Capitol Hill going to counter extortion when they have made it legal to extort campaign “contributions” as long as they do it from a private phone line?