The first compromise was a single seven-year term without eligibility for reelection, but that fell apart when delegates couldn’t agree how the president would be elected—by Congress, by the states or by the people?  
Left undecided, the question of presidential elections and term limits was referred to the Committee on Postponed Matters, which hammered out a novel solution. The president would be elected by “electors” chosen by each state (known, collectively, as the Electoral College) and would serve a four-year term. However, there were no limits placed on how many times a president could be reelected.  
Did presidential term limits remain a contentious issue?  
When George Washington stepped down after his second term, he established a powerful precedent limiting presidents to two terms. But politicians from all parties worried that their opponents might break with tradition and stay in office indefinitely.  
Before the 22nd Amendment, there were nearly 200 attempts by Congress to impose term limits on the president (the first as early as 1788). The closest Congress came to passing an amendment was during the presidency of Ulysses S. Grant when Grant’s Republican allies floated the idea of a third term.  
Instead of an amendment, the House passed a resolution warning that “any departure from [George Washington's] time-honored custom would be unwise, unpatriotic, and fraught with peril to our free institutions.”   
Did Congress pass the 22nd Amendment to prevent FDR from winning another term?   
The 22nd Amendment was definitely written in response to Franklin D. Roosevelt, the first president elected to more than two terms, but it was passed after FDR had died in 1945. Starting in 1932, Roosevelt was elected four consecutive times and served from the Great Depression through World War II. FDR died from a cerebral hemmorrhage not long after his fourth inauguration.  
Previous attempts to impose term limits had failed because constitutional amendments require a two-thirds vote of both houses of Congress. The 22nd Amendment passed because Roosevelt’s Republican opponents teamed with southern Democrats upset over Roosevelt’s liberal policies.  
Congress approved the 22nd Amendment in 1947, and the states ratified it in 1951.