As coverage of last week’s flare-up between Bob Woodward and the White House devolved into the granular parsing of words and implications and extrapolations and possible intent, the larger point was roundly missed: the increasing pressure that White House correspondents feel when dealing with the Obama administration — to follow their narrative, to be properly deferential (!), to react to push-back by politely sitting down and shutting up.

“The whole Woodward thing doesn’t surprise me at all,” says David Brody, chief political correspondent for CBN News. “I can tell you categorically that there’s always been, right from the get-go of this administration, an overzealous sensitivity to any push-back from any media outlet.”

A brief recap: After the Washington Post ran a Woodward op-ed in which he claimed that the administration was “moving the goalposts” on the eve of the potential sequester, the veteran journalist went on to assert that economic adviser Gene Sperling said, in an e-mail, “I think you will regret staking out this claim.”

While Woodward spent a lot of the week on cable news going back and forth on whether that was a threat, few reporters, if any, asked why a high-level administration official spent so much time — Sperling admittedly shouted at Woodward during a 30-minute phone call, followed by that e-mail — attempting to control an opinion expressed in a newspaper.

The answer, say former and current White House correspondents, is simple: This administration is more skilled and disciplined than any other in controlling the narrative, using social media to circumnavigate the press. On the flip side, our YouTube culture means even the slightest gaffe can be devastating, and so you have an army of aides and staffers helicoptering over reporters.

Finally, this week, reporters are pushing back. Even Jonathan Alter — who frequently appears on the Obama-friendly MSNBC — came forward to say he, too, had been treated horribly by the administration for writing something they didn’t like.

“There is a kind of threatening tone that, from time to time — not all the time — comes out of these guys,” Alter said this week. During the 2008 campaign swing through Berlin, Alter said that future White House press secretary Robert Gibbs disinvited him from a dinner between Obama and the press corps over it.

“I was told ‘Don’t come,’ in a fairly abusive e-mail,” he said. “[It] made what Gene Sperling wrote [to Woodward] look like patty-cake.”

“I had a young reporter asking tough, important questions of an Obama Cabinet secretary,” says one DC veteran. “She was doing her job, and they were trying to bully her. In an e-mail, they called her the vilest names — bitch, c–t, a–hole.” He complained and was told the matter would be investigated: “They were hemming and hawing, saying, ‘We’ll look into it.’ Nothing happened.”

He wound up confronting the author of the e-mail directly. “I said, ‘From now on, every e-mail you send this reporter will be on the record, and you will be speaking on behalf of the president of the United States.’ That shut it down.”

Neil Munro, White House correspondent for the conservative Daily Caller, says that after he interrupted Obama during a June 2012 press conference on immigration — inadvertently, Munro insists — he felt the wrath of the administration. “The White House called and bitched us out vigorously,” he says. “I haven’t been called on since shortly after Osama bin Laden was killed.”

“I’ve seen reporters get abused — but it’s the job of the press to push back hard,” says Ron Fournier, a White House correspondent under Bill Clinton and George W. Bush. “The people you’re covering don’t feel like they should be challenged, and they have immense resources at their disposal to beat back.”

CBN’s Brody, who covered Obama during the 2008 campaign and was granted four one-on-ones, has emotional whiplash from his treatment by top aides. On the one hand, he’s sympathetic: “I think they believe in a rabid defense of this president, who has had so many critics, at all costs,” he says. On the other, they are often bullies and a favored tactic is to make a journalist feel dumb, unsophisticated, unworthy of the job or the briefing room or the returned call.

“The way they treated Woodward,” says Munro, “is the way they treat other reporters.”

One correspondent says that when he inquired about a staging choice for the president’s speech, he was steamrolled. “There was one specific White House aide calling me up, yelling and screaming,” he says. “It was condescending and abrasive: ‘Why is this a story? Why are you doing this? This is of no consequence. You’re making a mountain out of a molehill.’”

This went on for two days. “All I wanted,” says the reporter, “was an answer to a question. It’s not like I was looking to do a 12-page exposé to take down an aide. It was unnecessary vociferousness.” He eventually got his statement.

Another White House correspondent says that last week’s blowup over pool reporters’ access to the president’s golf game with Tiger Woods — which was none — is indicative of a larger problem. “Today’s a perfect example,” he says. “Jack Lew is sworn in” — as US Treasury secretary, on Thursday — “and they didn’t even allow a photographer in there. A reporter asked [press secretary] Jay Carney why, and his answer was, ‘It’s a family ceremony.’ No! This is a high-ranking government official whose salary is paid for by taxpayers. No.”

“This administration has tools to reach people on their own,” CBS White House correspondent Bill Plante said this week. “They don’t need us as much. And to the extent that they’re able to do that, they’re undercutting the First Amendment, which guarantees a free press through many voices. If they put out their own material, it’s state-run media.”

Meanwhile, the increasingly obsequious Steve Kroft at “60 Minutes” has had more access to the president than any other reporter, and his last sitdown — with Obama and outgoing Secretary of State Hillary Clinton — was less a scrupulous exit interview than an infomercial for Hillary 2016. Kroft kicked off things by making it clear he had been summoned: “This is not an interview I ever expected to be doing,” Kroft said. “But I understand, Mr. President, this was your idea. Why did you want to do this together, a joint interview?”

“These are the two most influential foreign-policy officials in the United States,” wrote The Atlantic’s Conor Friedersdorf. “In the last four years, they’ve presided over hugely consequential policies all over the planet, much of it cloaked in secrecy.” He went on to excoriate Kroft’s soft-balling as “an embarrassing failure.”

None of the White House correspondents who spoke to The Post are hopeful that things will improve. “What’s our recourse?” says one. “How do you force them?”

“The reporters I’ve spoken to who have covered multiple administrations have said this is tighter, more restricted than other administrations,” Munro says. “They don’t like it. They don’t have the power to change it.”

For these reasons especially, Fournier is nostalgic for the days of covering Bill Clinton. “Every five or six days, he’d do a public event, and we’d go and yell questions and occasionally, he would answer,” Fournier says. “He had to be accountable to an a–hole like me. That’s healthy for democracy.”

mcallahan@nypost.com