"It is said "reality has a well-known liberal bias." [http://tr.im/owWY] Is it the case that reality "votes" for liberals more so than for conservatives, or is it "fair and balanced"?"The line is used frequently by Stephen Colbert as a play on the working the refs strategy of the right which is to brand the media as having a liberal bias, but taken seriously, I would say that the answer is yes and no.
There are certainly places that portions of the conservative movement do place ideology before science. The religious right's attack on the teaching of evolution, global warming, and their insistence on abstinence only sex ed are examples where they give just so stories that happen not to line up with the way the world works.
Another way in which one could claim that reality has a liberal bias is in the conservative rejection of social science. The appeals to personal responsibility are, as I've discussed here many times, a rejection of social/economic/political factors in shaping how people behave. If social factors play a role and they can be changed, then government programs and regulations would be necessary. Of course, sociological factors are meaningfully operative and in this way the liberal approach is correct. That is not to say that liberals do not often overstate the role, neglecting the autonomy of individuals, but the sort of wholesale rejection of the effect of systemic factors is flawed.
But, there is a way in which reality is often biased against liberals. The famine in Ethiopia and then homelessness in the US became well funded, high visibility causes in the 80s. You had rock festivals and big time media attention. Every organization concerned about alleviating suffering somewhere took note and as a result began to compete for the attention. You began to see an arms race of liberal causes, each trying to portray itself as the most pressing issue of the times. As a result, you needed to take quite legitimate problems and show them in their worst possible light in order to try to elevate your situation of interest. There is incentive, if not to exaggerate, then certainly to push worst case scenarios without making fully clear that they are not the most likely scenarios. As such, reality often does not match up with the most dire predictions of those who were seeking public attention to their cause.