I think claiming that the media is "dominated" by liberal voices is a stretch. Keep in mind that I'm in my mid-30s and Fox News has been the #1 rated cable news source for my entire adult lifetime. The most influential truly liberal voice we've had was probably John Stewart/Stephen Colbert and that was on a comedy network for one hour a night four nights a week. Colbert didn't even make sense without knowledge of Bill O'Reilly and Hannity.
If you defined everything to the left of Fox as "liberal" then the volume of stories are definitely "left of fox," but to be honest that just isn't the way the world works. Most newspapers try very very hard to have balance and say that both sides have valid points. This, paradoxically, has the effect of creating a right-ward slant because if you have to pretend that one side is making points that are just as valid as the other, even when they are not, it gives legitimacy and a greater voice to the weaker side. John Oliver did an excellent job demonstrating this effect as it pertains to Global Warming debates on television about a year ago and the Obama administration has had a nearly decade long problem with respect to the effect of long-term debt accumulation on this issue. Newspapers have been giving equal time to people predicting runaway inflation that has never materialized and we all pretend Paul Ryan is some kind of conservative budget genius because we need to create the illusion of balance. That illusion, created by pressure from people who constantly cry "liberal bias" actually creates a slightly rightward tilt.
This assumes it made sense to ask for "long form" birth certificates in the first place (I don't have one for me and can't get one).
That said, Ted Cruz this year has a shockingly similar birth story to Obama even if Obama had been born in Kenya (to be clear, all the evidence said he was born in Hawaii). Cruz was born in Canada to an American woman and a Cuban man. He was born with Canadian citizenship. That makes him a likely natural born citizen as a child of American born overseas. After all, he never had to go through a naturalization process. There is virtually no rumbling asking about Cruz, under shockingly similar circumstances, because no one on the left really cares outside of being sort of amused about the whole thing.
Hawaii eventually had to go through a very special process to produce the full long-form birth certificate. Unless you allege a conspiracy to put up red tape, there's no evidence that Obama had special powers to compel Hawaii to produce a different birth certificate than the one he could obtain through public means. In essence, Hawaii coughed up the long form only because everyone asked for it so many damn times. Good luck getting another Hawaiian long form certificate for any other citizen.
Left political candidates are regularly lampooned, although frequently for being weak, philandering, or being silly rather than for being stupid (comedians go where the joke is easiest). Bill Clinton was the topic of jokes (and still is) about his weight and his taste in women for decades. George McGovern in the tank jokes were staples of the late 1980s. Hillary might be the most viciously mocked candidate of them all. Probably the best-known political satire the last five years has been Obama's anger translator Luther. Claiming that SNL or other outlets only make fun of conservatives is a non-starter. It's not really the liberals fault that you've never had your own Colbert.