One could argue that Hamilton's elected president for life is little more than a dictator.  However, to argue that he is a monarch, is to suggest that the source of the authority of office is both divine and hereditary.  

That is precisely the opposite of what Hamilton proposed, and even that was enough to get him smeared as a monarchist.  In any case, Washington prevailed in that argument, until a certain Progressive, FDR, thought he knew better.  He didn't.  Now Bush will leave office, and neither his relatives, nor anyone from America's other, parvenu royal family (the Clintons), will replace him.

That suggests to me that even Hamilton's non-monarchy idea remains a fairly rare meme in the American memepool.

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I am the most conservative Unitarian-Universalist you will ever meet.