As things stand now in OTL, if a President of the USA dies or resigns during their term, their Vice-President replaces them for the entire remainder of their term. Several times, this has resulted in somebody elected Vice-President serving close to four years as President before having to be elected to the position. No matter what, the four-year election cycle does not change.
But what if things were different? What if, in the event of a President dying or resigning, a presidential election had to be held in
the very next available election cycle, even if the last one was only two years ago rather than four?
Let's take the example of the very first time this rule would have to be obeyed, making it the effective POD: President John Tyler, a.k.a. "His Accidency". Tyler was elected Vice-President in 1840 as running mate of William Henry Harrison. He served as Vice-President for thirty days in 1841, then served as President for almost four years afterwards until Harrison's term expired. If this rule were in place,
the very next presidential election would have been in 1842. Meaning that Tyler (who had been expelled from his party in September 1841) would have had to vacate the White House in March 1843, and someone else would be president. And from there the election cycle would go back to four years, meaning elections in 1846, 1850, 1854... (unless another president died early, in which case it would reset again).
Who could be elected in 1842? What would the consequences be from there, regarding the annexation of Texas, the South-West, the Oregon Territory? What about the Know-Nothing movement, the Free vs Slave state divide? How could these be affected?
Just for fun, here's some other examples of how this would've changed OTL history -- ignoring all butterflies between them, of course:
- Election in 1866 after Andrew Johnson succeeds Abraham Lincoln.
- Election in 1882 after Chester A Arthur succeeds James Garfield.
- Election in 1902 after Theodore Roosevelt succeeds William McKinley.
- Election in 1946 after Harry Truman succeeds Franklin Roosevelt.
- Election in 1974 after Gerald Ford succeeds Richard Nixon.