What evidence is presented by those who think the press has a liberal bias?

There isn't any. It is just a situation where one "news" agency is so far to the right that it lives in an isolated bubble, and defines any thinking to the contrary as a "liberal bias". The fact is that the whole country has moved moderately to the right, and that Reagan would be considered a liberal today. But we are not extreme right enough for Faux News, so we must have that liberal bias, which can only really be found at the "Nation" and the Huffington Post.