It is a 1st Amendment issue, though. You're literally calling for the state to sanction or prevent speech, based on the political slant of its content. This runs afoul of most 1st Amendment jurisprudence and, even if it isn't unconstitutional, is seriously problematic. Just imagine what a Republican would do: They'd use it to go after NPR and the New York Times. Recall that the Fairness Doctrine, before it was repealed, gave enforcement powers to the FCC... whose Chairman and commissioners are appointed by the president.

"If there be time to expose through discussion the falsehood and fallacies, to avert the evil by the process of education, the remedy to be applied is more speech, not enforced silence." - Justice Brandeis, Whitney v. California