Continue the 2nd term curse?

Between 1960 and 1980, no President completed two full terms in office.:
John F. Kennedy was assassinated in his first term.
Lyndon Johnson win in 1964, but declined to run in 1968.
Nixon won 2 terms, but resigned 2 years into the second term.
Carter lost re-election

To continue that trend to 2000 isn't impossible:
Reagan dies in 1987.
Bush fills out that term, gets elected in 88, but loses in 1992 --To Democrat Paul Tsongas.
Tsongas declines to run in 1996 because of the re-occurrence of his cancer and dies as OTL on Jan 18, 1997.
His VP, William Jefferson Clinton, runs and wins in 1996 (taking over as president in the last weeks of December 1996/early January 1997, as Tsongas declines.
He is forced to resign in 1999 after a sex scandal..

After 40 years with no completed second term, do politicians still try?
 
Political ambitions trumps silly superstitions.

Same with the Curse of Tippecanoe. Didn't stop Reagan in 1980, GWB in 2000, and whoever runs in 2020.

However, amp up the creepy and tie it to a specific event - the ratification of the 22nd Amendment - and you may have something that takes on a life of its own.

With China falling to the Communists in 1949 and Truman's rollback being a failure, along with a sketchy economy, Truman drops out early in 1952 as he did OTL. Going forward, any elected president is subject to the 22nd Amendment.

Eisenhower gets elected in 1952 and 1956 but has a heart attack in office and dies in 1959. The obvious way to go is to have Kennedy boot Nixon out in 1960 and still get shot, while LBJ declines to run in 1968 with Vietnam going quagmire. Nixon returns to the White House in '68 and '72 and resigns due to Watergate, and Ford takes over, loses to Carter, who loses to Reagan in 1980.

However, John Hinckley Jr. has a little better aim and Reagan does in 1981. HW takes over and finishes out his term, winning again in 1984 but clunking to the end of his term in 1988. Dole narrowly wins in 1988 but gets clobbered in '92 by Clinton.

Clinton wins again in 1996 but Lewinsky turns into a nightmare (someone here once proposed that, instead of just oral sex, Clinton got Lewinsky pregnant and it destroyed his presidency.) Clinton resigns before impeachment proceedings begin, and Gore loses by a wider margin than OTL.

Bush oversees the 9/11 recovery, but the president is hampered by a slow economy and the Diebold problem gets out of hand (in which a letter from Diebold voting machine company sends a letter that says it is "committed to delivering Ohio's electoral votes to the president" in 2004.) The scandal costs Bush Ohio, and Kerry loses the popular vote in 2004 but wins the EC.

A constitutional amendment is proposed to eliminate the EC with bipartisan support and clears congress in late 2005 with flying colors. It narrowly fails in the states, and the economy turning to shit in 2007 costs Kerry the election and John McCain is elected.

McCain is elected again in 2012, but he succumbs to brain cancer sooner and passes away in 2015. VP Mitt Romney takes over and narrowly loses to Barack Obama, the 50th President and the first non-white President, in 2016.
 
One thing was in 1984, beforce Reagan won re-election, there were opinions out there that the Presidency had become too complicated and draining for someone to manage two full terms
 
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