It's called Obama derangement syndrome (yes, there's a name for it). It's a belief I've heard numerous times during his presidency. However, this derangement syndrome is not exclusive to Obama. I heard people say the same thing about Bush Jr. and Bill Clinton (and, there is a term "Bush Derangement Syndrome"...I never heard this name associated with Clinton, but a lot of people opposed to him expressed those sentiments).
If you think about it, there are a lot of people on the extreme ends of the political spectrum that believe that a president they were opposed to will become a dictator and take away democracy. I wouldn't pay much attention to such rhetoric, considering that much of it is irrational talk.