The only issues where I'd say the news media is genuinely more liberal than the average American is gun control, and I'd say that has more to do with the fact that just about every person in the news media lives and/or works in a major City where gun violence is a problem. Considering gun control hasn't been a major platform issue of the Democratic party since the mid 90's, and is of little interest to the modern progressive/liberal movement (they are far more concerned with social and economic matters), it's hardly fair to classify them as across-the-board liberals.
It would be an interesting technology project or site. Do a sentiment analysis of major media sources. Search for how often a particular phrase is used. e.g.
Immigration: "Illegal Alien" or "Undocumented Worker"
Abortion: "Pro-Life" or "Anti-Abortion"
Something that could update in real time. It is unavoidable that every news site will have some slant, but an objective number based on rational criteria would be a good tool ala the nutrition facts labels on food packages.
In any event, I'm not sure it means much: most news organizations operate out of major cities, and major cities tend to have more liberal populations. If it was economically feasible to start a world-class news organization in a rural part of the Bible-belt, things might be different, but apparently it is not.
Neither a Democrat nor Republican, but find the ongoing pretense by many otherwise brilliant people that the dominant US media isn't left biased to be an incredibly silly rationalization.