The Fairness Doctrine was a Federal Communications Commission rule requiring over-the-air radio and television broadcasters to be fair and balanced (so to speak). For instance, if a TV station broadcast a station editorial, they had to allow anyone else (within reason) to present a contrasting view of the issue. Nowadays, some in the Democratic Party see it as a way to silence right-wing radio; such attempts are sometimes called "Hush Rush" movements, after Rush Limbaugh.
However, due to the negative connotations associated with the rule, it's probably not going to come back despite it being supported by some politicians. And, Barack Obama opposes it.
But, never fear, for the Democratic Party has a new trick up their sleeve. Instead of bringing back the FD, they support efforts that would have the same chilling effect. Obama and others oppose what they call media consolidation and support its related localism, i.e., enforcing ownership rules to give licenses to companies based out of the locations of their licensed stations. And, those plans are supported by the Obama-linked Center for American Progress; note that their blog ThinkProgress refers to mainstream talkers like Rush as "hate radio".
The bottom line is that the Democratic Party wants to reduce the influence of Rush and similar talkers, and they're going to try to do it using something that will have a similar effect as the FD but just not with the FD itself.
Unfortunately, some opponents of these plans hurt their case by outright claiming that the Democrats want to "bring back the Fairness Doctrine" instead of saying something like "they want to bring back something that would have the same effect as the Fairness Doctrine; it might be the FD with a different name, or it might use different tactics to achieve the same effect." The second is much wordier, but if something like that isn't used, Obama supporters will be able to deflect the impact by referring to the fact that Obama opposes the FD.