President Obama's White House has a troubled history with conservative and/or right-leaning media, and has done pretty much since the president took office. The rancor on both sides is generally equivalent.
Certainly, an equal amount of rancor was loosed this weekend from both sides, when President Obama criticized Republicans for being overly beholden to Fox News and radio host Rush Limbaugh, only to have one prominent Fox host fire back accusing him of thin skinned dishonesty.
First, there was President Obama's comment itself, which he made in an interview with the liberal magazine The New Republic (emphasis added):
Well, look, I've always believed that there are a bunch of Republicans of goodwill who would rather get something done than suffer through the sort of nasty atmosphere that prevails in Washington right now. It's not a fun time to be a member of Congress.
And I think if you talk privately to Democrats and Republicans, particularly those who have been around for a while, they long for the days when they could socialize and introduce bipartisan legislation and feel productive. So I don't think the issue is whether or not there are people of goodwill in either party that want to get something done. I think what we really have to do is change some of the incentive structures so that people feel liberated to pursue some common ground.
One of the biggest factors is going to be how the media shapes debates. If a Republican member of Congress is not punished on Fox News or by Rush Limbaugh for working with a Democrat on a bill of common interest, then you'll see more of them doing it.
This mention of Fox by name prompted an angry reaction from Fox host Greta van Susteren, who fired back on her blog with the following criticism:
Apparently President Obama wants his usual media pass and Fox challenges his policies – which happens to be the media’s job.[...]
And do you know what else? Brace yourself for this one! Some Democrats have told me that they want to come on Fox to discuss issues but they get heat from their Leadership for appearing on Fox. Does President Obama know that? So which Party is intimidating its members? And to say Senator Harry Reid is willing to compromise is just wrong. He has not allowed a budget to get to the Senate Floor for years to even begin a discussion. The budget process is where all compromise begins and ends and ended it before it even got started.
This is not the first time the Obama administration and Fox News have clashed. Back in 2009, White House spokesman Anita Dunn called Fox "opinion journalism masquerading as news," only to be blasted by the network's hosts repeatedly, and scathingly memorialized by Fox News contributor Andrea Tantaros when she (Dunn) left the White House.