I think if this "unfair doctrine" had more of a chance of passing, there would be more of an uproar about it. Frankly, I don't think it has a chance in hell of passing... even the new renamed version.
If it does pass it ought to be held unconstitutional. Previously, the Supreme Court upheld it specifically because of the limited channels of communication. If there was a limited amount of space for information to be provided, and not many places to find alternative points of view, then the rationale becomes stronger.
We're so awash in information of various points of view these days that the original rationale used by the Supreme Court doesn't apply any more, and since that was the basis for upholding I think there's a good chance the courts looking at it now would say it was unconstitutional.
After all, it is not only a prior restrain on speech, but a prior restraint on Political speech. That gets just about the toughest scrutiny of anything the government can do, and courts are only supposed to allow such things if they are 'necessary.' In this case, the necessity isn't there any longer because we have so many information sources available to us.