Obama didn't specifically introduce NN, but the FCC's three democrats did, and he supported it and he appointed his Chairman (I forget who) who everyone knew supported it.
The law in this area is all... old. Title II covers "telecommunication services" and has strict regulatory requirements. The FCC has authority to make rules for Title II telecommunication services, but not information services. That, the FTC (a much weaker agency) can sort of police not by setting rules by buy suing companies if they mislead consumers.
But this law wasn't passed when there was anything like what the internet is, and in the days of the likes of AOL and CompuServe and such, it made sense for the internet to be looked at as an information service.
But the internet is a whole lot more now, and most of the country has access to it via state-granted monopolies, there's no competition in it. So Obama's FCC ruled that it was a Title II telecom service. Some people claim that was an overstep of their authority, but that's questionable -- the law doesn't define what a telecom service *specifically is*, see. Its sort of up to the FCC to define what exactly qualifies as a Title II service.
Now this could all be fixed by Congress passing a law that actually made sense for the modern internet, buuut, the Republicans want no regulation on it at all so they get what they want this way.