Fox News correspondent Ed Henry on the front lines with President Obama

"Like every other professional journalist who covers the White House, we don't like every word that Ed has said on camera, but we work with him every day to provide the access and information that he needs to communicate to a sizable audience what's happening at the White House," said White House spokesman Josh Earnest.

Benghazi has proved an interesting case study. Henry rejects the notion that he works off Fox marching orders in discussing the issue, but said, "I wouldn't lie to you. I see that we're covering Benghazi a lot, and I think that should be something that we're asking about."

He said other news outlets have under-covered the story, since four Americans were killed and there's still some mystery about what the administration knew and when they knew about the attack.

Henry is keenly aware of the "noise machine," bloggers like Media Matters who quickly pounce on work they consider objectionable. He suggested that MSNBC host Chuck Todd, who also works for NBC News, doesn't get the same level of critical attention paid to his work even though MSNBC is clearly slanted left.

As a young reporter, Henry said he looked up to former White House correspondents like Sam Donaldson, famed for shouting questions at President Ronald Reagan. "Now if you shout a question at Obama, you're somehow seen as a bad guy," he said. "I think some people have been cowed."

Donaldson, now 78, recalled angry letters he had gotten from Republicans about his coverage of the Reagan administration. When he covered President Bill Clinton's second term from ABC and asked tough questions, Republicans wrote to compliment him on his maturity, he said.

He had his boss' support and didn't have to look over his shoulder at blogs, said Donaldson, who considers Henry "one of the best" on the beat now.

"It's not that they are all afraid and cringe, because they don't," Donaldson said. "But it's so much tougher to do it in every way."

His advice on dealing with the critics: "You just have to try to ignore them."

Henry said he tries.