As we know, Fox "News" is the mouthpiece of the Republican Party, serving approximately the same function that Pravda used to for the Communist Party in the Soviet Union. (Roger Ailes who runs FNC used to be a media consultant for the Republicans, working to get favorable coverage for his party in the news media of the day. But now he has his own network to push party propaganda practically 24 hours a day.)*
For a while back in 2009, the White House called out Fox on its distortions, but in typical wussy fashion backed off when Fox objected. And one could argue that the White House should not be using taxpayer money to defend itself against media attacks from a specific source.
But there is no reason the DNC could not work to expose the distortions coming from Fox. I would suggest that the DNC set up a dedicated website just to report on Fox's untruths - call it say "Fox's Daily Distortions" - and list on it all the misstatements and unfair rhetoric put out by Fox in the previous 24 hours.
But will they? Not a chance.
(And yes, from time to time I've sent messages to the DNC with suggestions on improving the Democrats' messaging. I've not once received an acknowledgement.)
* I'll acknowledge that there are interruptions to the propaganda mill, such as Shep Smith's reports