I know it's hard for some to believe, but Fox News has only been around for 20 years. Before that, you had the NYT, WaPo and sometimes the LA Times or Boston Globe as your primary newspapers. You know, back in the day when people didn't have the internet and actually read newspapers. That is where all the serious journalism came from, and where any big stories would break. The big stories would then be pushed on the big three networks-- NBC, ABC, and CBS. That presumes that the big networks didn't break their own stories. CNN was obviously in play too, and became a more serious player around 1990 with the Gulf War.
When the GOP rails against the mainstream media, it pretty much means that, you know, mainstream media that existed prior to the advent of Fox News, which came about directly as a result of mainstream media bias and filled an enormous void for disgruntled conservatives fed up with biased reporting. The mainstream media continues to lean left (I would argue they are more left now than ever, as gloves are off in this election). The difference is that the mainstream media has a waning (but still powerful) influence due to the internet and availability of wide sources of information. The Pubs still haven't figured out social media very well, though, and that's where most influence will be felt if not now then shortly in the future.