Democrats don’t avoid Fox as some kind of sop to the MoveOn.org crowd. They do it for the same reason they limit their press availability in general: because they’re afraid of getting tripped up, caught in a flip-flop or a contradiction.
But this isn’t quite right, in my view. It’s true that, as Jeff says, Democrats are more likely to get tripped up during an interview on Fox News than on other networks. But they didn’t start consistently snubbing Fox until liberal activists, led by watchdog groups like Media Matters, made it into an issue. (You can call that "pandering to the far left wing", as Mr. Wallace does, or listening to the wishes of your supporters, or whatever you like, but it’s how politics works.)
Those groups came to realize that, by treating Fox like any other network, Democrats were legitimizing it in the minds of ordinary voters as a "fair and balanced" news outlet. In the long run, that does more to damage Democrats, and progressive causes generally, than would passing up a chance to speak to its audience. Better to draw a firm line in the sand, so that, outside of the one-third or so of Americans who self-identify as ideological conservatives, Fox would continue to be seen as skewing right.
Trying to play nice with Fox, Democrats have concluded, is like trying to play nice with Rush Limbaugh–it’s a game they believe they’re never going to win. Instead, they’ve decided to launch a challenge to Fox’s credibility. To me, that seems like smart long-range politics.