No. There was no limit.

However Washington had refused to run for a third time (for complex reasons), and this had set a tradition that Presidents should only remain in office for 8 years. For 150 years this tradition was respected. It became an "unwritten rule".

FDR broke this tradition when he ran again in 1940. The context was one of impending war; hostilities were already well advanced in Europe and Asia, and it seemed likely that it would only be a matter of time before the USA was drawn in, just as it had been in the First World War. It seems that he believed he was the only person suitable to hold the Presidency in the emergency. (There were other complexities, if FDR had stood down in 1940, a Southern Democrat rather than a New Deal Democrat might have become the Presidental candidate, so there were internal Democrat politics as well as great world events.)

No. There was no limit.

However Washington had refused to run for a third time (for complex reasons) as did Jefferson, and this had set a tradition that Presidents should only remain in office for 8 years. For 150 years this tradition was respected. It became an "unwritten rule".

FDR broke this tradition when he ran again in 1940. The context was one of impending war; hostilities were already well advanced in Europe and Asia, and it seemed likely that it would only be a matter of time before the USA was drawn in, just as it had been in the First World War. It seems that his party believed he was the only person suitable to hold the Presidency in the emergency. (There were other complexities, if FDR had stood down in 1940, a Southern Democrat rather than a New Deal Democrat might have become the Presidental candidate, so there were internal Democrat politics as well as great world events.)