This is a bit of a mashup question.
This portrait is featured prominently in the office of Francis “Frank” Underwood (Majority Whip in the U.S. House of Representatives) in Netflix's original series House of Cards.
I’d love for the history junkies of /r/AskHistorians to not only identify who this is a portrait of (my guess is George McDuffie (D)), but, more importantly, how this individual may relate to Underwood, the Machiavellian protagonist anti-hero in the series.
The symbolic use of other portraits throughout the series is far more self-evident (e.g., portraits of LBJ, and Andrew Jackson), but here I think /r/AskHistorians could have a little fun both identifying the individual in the portrait and providing some rich historical context to their life, further informing the narrative of the series. There is already a thread going on right now in /r/HouseOfCards, but the users over there lack the historical knowledge and context to both identify who this is a portrait of, and what the use of this person's likeness could symbolize.
This is purely a guess, but perhaps John Henry Eaton? Senator Eaton had ties to both Andrew Jackson (personal friend and served him as Secretary of War) and John Calhoun (famous South Carolina senator/vice-president). Calhoun's bickering with President Jackson resulted in the former's resignation (the first to do so). The wives of Eaton and Calhoun despised each other too, with Floride Calhoun accusing Mrs. Eaton of having an affair with Eaton before his first wife had died (Petticoat Affair).
As an aside, I view House of Cards more as Macbethian (if that's even a word) than Machiavellian.
While Frank Underwood is presented as the archetype of a self-serving, amoral and power-hungry politician, it does not do justice to Machiavelli's philosophy at all. In the common usage, the Machiavellian adjective vilifies and places the character Frank as some kind of anti-hero that, by the unbound power of his amorality and pure will, is able to ascend the stairs of power.
In fact, Machiavelli's an advocate not only for the wise application of the power of the Prince, he places politics as a realist landscape, a field of human conflict where hard facts matters and not holier-than-thou sentiments or morals must dictate action for the good of all. His vision is unclouded by the supposedly natural goodness of man and argues for a true republic of citizens.
Of course my interpretation is very much simplified.