In 2004, New York Times writer Alessandra Stanley described Fox as "the conservative cable network", and Fox immediately called for a retraction. If you want the money, power, and influence that comes from being a network with a broad audience, you can't let yourself be regarded as the provider of a niche product, and a politically biased niche product at that.
In addition to the immediate benefits of cancelling the Fox News debate in Nevada -- we won't have to deal with conservatives immediately framing the Democratic candidates' views in a negative light -- I'm hoping that this will be the beginning of the marginalization of Fox News. If Fox keeps getting this kind of treatment from Democratic leaders like John Edwards, whose decision not to participate was instrumental to the debate's collapse, it'll be a lot easier for reporters to rightly tag Fox as conservative. I hope for a situation where even the most politically tuned-out viewers are on guard against Fox's conservative bias, and people choosing channels for a TV in a public area will see picking Fox News as a strong political statement that they probably don't want to make.