Updated

Conservative media critics are pushing back on President Obama's suggestion that Capitol Hill Republicans would be more inclined to work across the aisle if they were "not punished" on Fox News and other outlets for doing so.

The president made the comments in an interview with The New Republic, when describing the difficulties in crafting bipartisan legislation.

"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," he said. "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," he said.

The criticism of certain media outlets comes after Obama struggled to strike a comprehensive fiscal deal and faced early resistance over his new gun-control proposals.

Bob Lichter, president of the Center for Media and Public Affairs at George Mason University, said Obama is just using an old Democratic Party tactic of saying, "centrists would go along if those nasty conservatives don't beat them up."

"I don't hear Obama complaining about The New York Times trying to pull him to the left," added Lichter, a communications professor at the Northern Virginia university.

Author and syndicated columnist Ben Shapiro said Obama trying to challenge certain media outlets dates back to the start of his administration.

"He's talking about silencing members of the media he doesn't like," he told Fox News. "He's done that before -- this idea that Fox News is some sort of evil force in the media.  He's gone after Rush Limbaugh, talked about starting boycotts. This is what he does. He's a bully."

"What he's saying is the media is not liberal enough. I think he wants people who don't like him to be quiet," said Shapiro, editor-at-large at Breitbart News.

Obama, in the interview, further argued that House Speaker John Boehner wanted to reach a deal on recent fiscal issues but couldn't in part because he was vulnerable to attack for compromising Republican principles and working with the president.

The president claimed the "more left-leaning media outlets," on the other hand, "recognize that compromise is not a dirty word."

Obama suggested that he, Senate Majority Leader Harry Reid and House Minority Leader Nancy Pelosi are more willing than Republican leaders "to buck the more absolutist-wing elements in our party to try to get stuff done."

The last time Obama criticized Fox News by name was on July 13, 2012.

"So just in case some of your friends or neighbors, or Uncle Jim, who's a little stubborn and has been watching Fox News and he thinks that somehow I raised taxes -- let's just be clear:  We've lowered taxes for middle-class families since I came into office," the president said at a campaign event in Virginia Beach, Va.

“The media has always helped shape the political environment,” said Rich Noyes, research director for the Washington area-based Media Research Center. “But Democrats object to the conservative media now being able to. … Liberal news outlets try to punish conservatives for their views on guns or cutting spending in ways that they think are cruel. It was so much easier for them when the big three networks and The New York Times left out the inconvenient facts. (Obama’s) trying to play games here.”