I think FDR was in office for 3 terms. He died in office or he would have served for 4 terms. The 22nd amendment was passed in 1947 which limited a president's tenure to 2 terms. Many people were afraid that Obama was going to challenge that amendment and stay on for another term. I don't think he even contemplated the idea, but some of the democrats might have. In this era of false news who knows what is true and what isn't.
The point of the 22nd amendment is that it would be difficult (or unconstitutional) for a president to become a dictator. That was the basis of the fear people had.