GOP candidates are used to duking it out with the mainstream media, but Donald Trump is getting it from all sides.

Now, one of the most powerful moguls is taking aim at Trump, reports CBS News correspondent Jan Crawford.

Some call it a grudge match between the two billionaires - media tycoon Rupert Murdoch versus the flamboyant dealmaker, who also happens to be a leading candidate for president.

"From the very beginning, Rupert Murdoch has been skeptical and concerned about a Donald Trump candidacy," said Gabriel Sherman, author of "The Loudest Voice in the Room."

Murdoch hasn't tried to hide it. On Twitter, he rails against Trump.

When is Donald Trump going to stop embarrassing his friends, let alone the whole country? — Rupert Murdoch (@rupertmurdoch) July 19, 2015

But the gloves really came off when one of Murdoch's premier properties targeted the Donald.

"This is one of the worst trade deals," Trump said at the most recent Republican debate.

Following the debate, the Wall Street Journal - owned by Murdoch - wrote in an editorial that Trump's take on the trade deal was flat-out wrong.

"It wasn't obvious that he has any idea" what the deal involves, the paper wrote.

Trump - in the Journal's words - "went bananas" over the editorial.

"I'm suggesting that the Wall Street Journal editorial board doesn't know what they're talking about, that they're third rate," Trump said on Fox Business Network, which is also owned by Murdoch and - despite Murdoch's efforts - continues to give Trump a big platform.

"You have all of these, you know sort of titans at the height of their game are all dancing around each other," said Sherman. "So far... no one has been able to take (Trump) down."

Or count him out. Complaining he had "been treated very badly," Trump met last week with the Journal editorial page to try to clear the air. The paper said it got "the full Donald."

"The Wall Street Journal is seen as representative of or close to business," said Republican strategist and CBS News contributor Frank Luntz. "And business is not happy with Trump when it comes to trade, immigration and other issues."

Trump's numbers were slipping, but the world changed with the Paris attacks and his message again is resonating with the people.

The latest polls show him with a commanding lead and voters who lean Republican say they overwhelmingly trust Trump to deal with the threat of terrorism.

Trump's kept the upper hand in part because he's not dependent on traditional conservative media. He takes his message directly to voters on Twitter, and he's found an audience with anti-establishment conservative commentators - like Ann Coulter, Mark Levin and Laura Ingraham.

The night of the Paris attacks, Coulter declared: "Donald Trump was elected president tonight."

They can wait if they like until next November for the actual balloting, but Donald Trump was elected president tonight. — Ann Coulter (@AnnCoulter) November 14, 2015

And on her radio show, Ingraham gives him a warm welcome. "Where is President Trump on ground troops -- another American ground force in the Middle East?" she asked him in a recent appearance on the show.

"Well, President Trump is for knocking the hell out of ISIS and doing it rapidly and also getting other people to do it with us," Trump answered.

Right now, those voices are striking a chord, and even the Journal is acknowledging Trump's staying power.

"Maybe it's time to start imagining Mr. Trump, come January 2017, in possession of the nuclear launch codes," the paper wrote.

"So many people in the business community and the Wall Street Journal never thought that he would do as well as he's done or would be able to sustain that success. They waited too long and they may be too late," Luntz said.

The next line of attack on Trump is from super PACS - millions of dollars of ads are expected to drop in the next month or so.

But as Luntz said, the remarkable thing about Trump is the more negative things said about him, the more his supporters like him.