I have to disagree with your argument in the second to last paragraph. A McCain staffer sent a memo saying that McCain and a female lobbyist were spending a lot of one-on-one time together and it could be portrayed as him having an affair. Basically a "Heads-up" memo. The NY Times used that memo to run front-page stories for at least a week trying to imply McCain had had an affair. When John Edwards HAD A BABY with Ms Hunter (the story was broken by the National Enquirer?!) the NYTimes and most other mainstream media outlets ignored it for WEEKS until they just couldn't ignore it anymore, then they ran low-key puff-piece stories and buried it. They WILL bury a good story to advance a liberal agenda. http://www.mrc.org/BozellColumns/newscolumn/2008/col20080812.asp
It is worth addressing because it is an argument I encounter often on this topic and it contains some elements of truth, or at least that could reasonably be construed to support the Left Wing Bias theory (which is not untrue precisely, just wildly exaggerated).
First, it is important to understand that the McCain story in the Times was a lousy bit of work, but I don't think it was a partisan question - it was just a garden variety stretch for a lead that failed miserably. As a journalist, I read that and understood what the authors were aiming for, but I also saw immediately that that they had completely blown any chance of making their point - which was that McCain was excessively cozy with a lobbyist despite the fact that he had spent years decrying the corrupting influenced of lobbyists - by allowing themselves to be seduced into playing up the unsubstantiated romantic angle. Obviously we can't tell what was in the minds of the authors and editors, but almost certainly it was an ill-advised structural decision rather than a partisan one.
But more importantly, the McCain-Edwards comparison falls apart because of the relative importance of the two characters - McCain was a serving senator, a presidential nominee, and the effective head of one of the two major political parties. And he has made a major issue of attacking the corrupting influence of money and lobbyists in Washington, so any entanglement with a lobbyist, whether romantic or not, is a matter of legitimate analysis (and that was actually the thrust of the Times piece, though they totally obscured the point with their stupid insistence of hinting at a romantic liaison). Edwards, by contrast, was a two-time failed political candidate who was out of public office for the foreseeable future. He was still a figure of interest to the public, of course, but his importance was far less, not even remotely comparable to McCain's. Couple that with the mistaken, but understandable, reluctance of major media to follow the National Enquirer and the picture becomes much more clear. Had Edwards been the nominee, or were he headed in that direction, when the story broke, I guarantee that the media play would have been entirely different (and this is why Democrats were so hurt and angry, probably, since Edwards' recklessness could have ruined the party had he been the nominee).
Unfortunately, the notion that the media has a sharp and deliberate leftward tilt is now so entrenched than a human failings and poor decisions, such as the one that afflicted the Times on their terrible McCain story, or the one that left mainstream news organizations trailing a supermarket tabloid, do begin to look like evidence of some dark conspiracy.
But that is reading far to much into the way the media works. The real answer is much more mundane, and that is that Edwards just wasn't as interesting a story, politically speaking, even if the tale had a bit of sex and hypocrisy in it. In 20 years in newsrooms of both a leftward and rightward orientation, I have never seen a decision made in the manner conservatives suggest. It just doesn't work that way, fortunately.