I've always found the claim that the "mainstream" media is biased to be absurdly off the mark. In fact, it is just the opposite, with the mainstream media continually producing "balanced" pieces that select equal numbers of examples from both sides regardless of the actual number of each (for example, climate science experts), and often entirely ignoring the progressive political wing. If you need an overwhelming example of the latter, just compare the attention that Paul Ryan's annual budget proposals receive relative to those put forth by the Congressional Progressive Caucus, which consists mainly of the more liberal third of the Democratic House delegation. According to a simple Google search, Ryan's budget has about 650 times as many hits as the CPC's "The Peoples' Budget", and even several times the 25 million hits one gets for "President's budget". Clearly, in this matter, the Republican budget proposal gets far, far more attention than those produced by the progressive wing, and even several times more than the formal and very centrist compromise budget put forth by the president himself! Admittedly, some of that attention is deservedly negative, but politically the ensuing conversation is a substantial net positive for Republicans.
What could possibly be the explanation for the vast discrepancy in media attention? It is certainly not because the Ryan budget is more realistic. If adopted, it would be by far the most right-wing budget of any advanced nation, and is unprecedented on many levels. It is also a complete fantasy in terms of how it works, with budget balance only achieved through heroic growth assumptions, budgetary gimmicks, and enormous cuts to anti-poverty programs and domestic spending that are both cruel, stupid, and unfair. Indeed, the poor would bear some 69% or more of the budget balancing directly. In contrast, the CPC's budget is very European-like in terms of spending and taxation, spreads the pain around evenly, and balances the budget in a reasonable time frame under realistic assumptions. The President's budget would actually be considered quite conservative by world standards and while failing to achieve budgetary balance, is realistic with respect to what is actually politically possible.
So the media in this case is clearly ignoring the actual left entirely, lionizing the right wing, and putting up a milquetoast centrist compromise as the left pole. This obviously distorts the debate and continually drags it to the right - something completely inconsistent with the theory that the mainstream media is liberally biased.