The shortest set term for a political leader I can find is the President of the Swiss Confederation - which is a one year term. But this person is simply a member of a seven person council and ultimately the council is a collective Head of State. People can serve on the council for as long as they remain elected - for periods of four years by the assemblies - and usually the VP one year becomes President the next, and only four times have sitting members of the council been voted out. Could something like this have worked for the early US - after all the Swiss model has been ?
As an example - (and also attempting to include a clause where a President can't have the same VP more than once - which would theoretically allow for a fairly hefty number of combinations without any swap-outs)
April 30th 1789 - March 4th 1781 : President George Washington, VP John Adams
81/82 : President John Adams, VP Benjamin Franklin
82/83 : President Benjamin Franklin, VP Alexander Hamilton
83/84 : President Alexander Hamilton, VP John Jay
84/85 : President John Jay, VP Thomas Jefferson
85/86 : President Thomas Jefferson, VP Jame Madison
86/87 : President James Madison, VP George Washington
87/88 : President George Washington, VP Benjamin Franklin
88/89 : President Benjamin Franklin, VP John Jay
89/90 : President John Jay, VP James Madison
90/91 : President James Madison, VP John Adams
* - shortly after the commencement of James Madison's second term as President of the Continental Council, Council Member Benjamin Franklin dies. With a position vacant, the National Assembly of Representatives appoint James Monroe to the Continental Council.
91/92 : President John Adams, VP Alexander Hamilton
92/93 : President Alexander Hamilton, VP Thomas Jefferson
93/94 : President Thomas Jefferson, VP George Washington
94/95 : President George Washington, VP Alexander Hamilton
95/96 : President Alexander Hamilton, VP James Madison
96/97 : President James Madison, VP James Monroe
98/99 : President James Monroe, VP George Washington
99/00 (i) : President George Washington, VP John Jay
99/00 (ii) : President John Jay, John Adams
* - almost three quarters of the way though his fourth term as President of the Continental Council, Council Member George Washington dies. With a position vacant, the National Assembly of Representatives appoint John Quincy Adams to the Continental Council. He is the son of current Council Member, John Adams - an amendment to the Constitution is made that if two people of close relations are on the Continental Council at the same point, they may not serve as President/Vice President together. John Jay immediately commences his new tenure as President, finishes out Washington's term and then continues through his originally expected term.
00/01 : President John Adams, VP John Jay
01/02 : President John Jay, John Quincy Adams
02/03 : Presidnt John Quincy Adams, VP John Jay
03/04 : President John Jay, VP James Monroe
04/05 : President James Monroe, VP John Adams
* shortly after the commencement of James Monroe's second term as President of the Continental Council, Council Member Alexander Hamilton dies. The National Assembly of Reprentatives appoint Andrew Jackson to the Continental Council.
05/06 : President John Adams, VP Thomas Jefferson