Given the conservative agenda, they will always see the media as liberal. The problem is, the media doesn’t report what should be but, instead, report what is. (The media that matters, anyway.) The same is true of education (but I won't bother to make that argument in this post).
We can compare the "liberal" media with conservatives on two topics: abstinence-only education and poverty.
For a good reporter, there would be no obvious solution to the problem of teen pregnancy. A really good reporter wouldn't even automatically accept the notion that teen pregnancy would itself be a problem. (It would make a great story for some reporter if he could report that teen mothers were actually happier than older mothers and their children went on to have better lives. What shocks conventional wisdom makes for better headlines.) If it turns out that sex-education that suggests but does not rely on abstinence turns out to more effectively protect teens from STDs and unwanted pregnancies, this is the story a good reporter will file. Outcomes dictate the story.
For the conservative, outcomes don't matter. Unmarried teens having sex is wrong. If sex education that explains the use of contraceptives and takes the stigma out of sex encourages even one more teen to have sex, it is a bad thing. The numbers, or facts, surrounding the occurence of disease or pregnancy don't matter. The story is not what happened but what should happen.
A similar thing happens with poverty. For the reporter, statistics matter (or ought to). Some policies lift more people out of poverty than others: the numbers of unemployed and homeless go down in the wake of certain tax and spending policies or education and outreach programs.
For the conservative, being homeless or unemployed is more likely to be a story of morality. If someone gets sick and is uninsured, they should have taken better care of themselves (do you see how fat those poor people tend to be?), or should have put more effort into a career and been able to afford insurance or ...
For the reporter, the story of poverty is objectively reported as changing in reaction to certain kinds of policy choices: theocracies, anarchies, and totalitarian regimes create more poverty than democracies, for instance, and democracies with welfare states have less poverty than democracies with no safety net. For the conservative, there is no question about what policies are best (fewer taxes and less government), therefore a rise in poverty offers a lesson to people to be more careful, industrious, and better at saving. It never calls into question which policies ought to be enacted, though, because those are already known.
Given that conservatives care so deeply about what SHOULD be and less about what is, they'll always see good reporting as having a liberal bias.