Assuming you consider the antiwar stance "liberal," the clearest example of this I've seen is a study of the media stories leading up to the Iraq War. 71% of US sources were pro-war, 26% "neutral," and 3% antiwar. When "both sides" were presented, it was pro-war vs pro preparing more for the war.
My mistake. Nobody was discussing the media having a bias towards any political party, they were discussing the media having a conservative bias despite Republican's claim of a liberal bias. Like when the antiwar position gets 3% of the media coverage.
Who are not conservative. It's just a misleading label. It has liberal roots. The Trotskyite past of its founders and prominent figures is interesting to note as well (e.g. Irving Kristol).
https://fair.org/extra/amplifying-officials-squelching-disse...