The framers who wrote the constitution originally stated that the president could serve

Unlimited 4 year terms.

Explanation:

Some of The framers wanted a presidency that was a life time appointment. Alexander Hamilton and James Madison wanted a lifetime president. They were in support of a presidency that was appointed by the Congress and not by the people. This did not pass.

Instead it was made that voting for the president was not entirely in the hands of the voting citizens but also in the hands of the electoral college.

The presidency was then shortened to a 4 years term but there was no limit to how many of this terms a president had to serve.