Pretty much what it says on the tin. Look at past men and women who plausibly could have been PotUS, either through election, or through the President dying at the wrong time (FDR was pretty unhealthy for all his terms), and would have done a horrible job at it (to continue the FDR example, I have little faith in Henry Wallace, who was VP for a while during WWII).
1) John Jay (1735-1829). Came third in elections of 1788-1789. I don't think the guy was incompetent, quite the opposite. But he was a prominent abolitionist, the founder of the New York Manumission Society, and an an advocate of boycotts against all businesses involved in the slave trade. Which caused much controversy within New York. With such militant views, I would expect an ideological conflict to begin.
2) George Clinton (1739-1812). Came third in the elections of 1792. A prominent leader of the anti-Federalist faction. But there are three factors that would make him a particularly poor choice for President. A) He was more devoted to the interests of New York, than to the entire country. "The governor would put New York concerns above all others" , B) He was one of the most vocal opponents of the United States Bill of Rights (1789) and favored amendments which would limit its influence over the various state of the Union. In favor of their own laws. C) His commitment to fair elections was somewhat questionable. His re-election as Governor of New York in 1792 produced a scandal of electoral fraud, "the destruction of ballots from Federalist-dominated Otsego County on highly suspicious technical grounds by Antifederalists canvassers". See:
http://www.senate.gov/artandhistory/history/resources/pdf/george_clinton.pdf
His election could result in the early demise of the Constitution of 1789, the return to to the style of the Articles of Confederation (1777) which he strongly favored, a weak federal government and highly autonomous state governments. Plus some policies which could only favor the interests of a single state: New York. Particularly banning or reducing the national tariff, another of his favorite causes. A tendency towards dirty politics might set the climate for his term.
3) Thomas Pinckney (1750-1828). Came third in the election of 1796. Widely considered at the time the most successful of the American diplomats. However his mere presence on the ballot caused concerns within the Federalist Party. Fellow candidate John Adams strongly suspected that there was a plot to eject him from party leadership and elect Pinckney in his place. Suspecting Alexander Hamilton (1755-1804) as the man behind the plot. "The essence of the 1796 plot thesis is that Hamilton and his friends, although ostensibly supporting Adams for President and the South Carolinian Thomas Pinckney for vice president, tried to have Pinckney come in first. The alleged reason was that Adams was ... too feisty to be controlled". ... There was much tension between Adams and Hamilton even following the victory of the former. And among their supporters. There were fears that the Federalists were about to split over the matter. See:
http://books.google.com/books?id=96...=0CDQQ6AEwAjgK#v=snippet&q="Pinckney"&f=false and
His election could cause the immediate split of the Federalist Party and some bad blood among its former leading figures. Pinckney himself was noted for his lack of association with any "radical" causes. But his contemporaries considered him as easily influenced by more experienced politicians. Modern historians suspect that he would serve as a mere puppet to Hamilton. Setting a bad precedent of "shadow presidents". See:
http://books.google.com/books?id=96...=0CDQQ6AEwAjgK#v=snippet&q="Pinckney"&f=false
