"The fury now is by the president," Axios' Mike Allen says of Trump's reaction to Steve Bannon

President Trump is threatening to sue his former chief strategist, Steve Bannon, for criticizing the president and his family in an upcoming book, "Fire and Fury." In explosive excerpts of Michael Wolff's tell-all book on the Trump White House, Bannon calls the June 2016 campaign meeting with a Russian lawyer at Trump Tower "treasonous" and "unpatriotic." The White House pushed back with a scathing statement saying Bannon has "lost his mind."

"We can see in their reaction that the fury now is by the president," Axios co-founder and executive editor Mike Allen said Thursday on "CBS This Morning." "I'm told that yesterday in the West Wing, people tried to avoid the president sort of the way you stay away from your dad when he's had it. He was so angry about this book, and what did he do? He called lawyers."

Sending a cease-and-desist letter to Bannon, the Trump lawyers told Axios in a statement: "Legal action is imminent."

The president's lawyers also went after Wolff and his publishers with a demand that they they halt publication and issue a public apology.  

According to Axios, Bannon told friends he would run for president in 2020 if Mr. Trump does not. Bannon said this knowing the book would include his argument that the special counsel investigation into potential collusion with Russia during the campaign could topple the president. Bannon suggests in the book that the Mueller probe is "all about money laundering."

Mr. Trump hit back in a statement saying: "Steve Bannon has nothing to do with me or my presidency. When he was fired, he not only lost his job, he lost his mind."

Allen, who interviewed Bannon last week, said Wolff has "dozens of hours of tapes" of interviews with staffers "that's going to make it so hard for these people who have been captured with these embarrassing and revealing comments to now deny them." A lot of them thought they were talking off the record, Allen said.

While the White House said they gave little cooperation to Wolff, Allen said Wolff actually had "unbelievable access" over several months.  

"The White House says that he was formally cleared in the White House less than 20 times, but for someone who's going into private areas of the White House including the then-chief of staff's office, Reince Priebus' office – that's a lot! And during those early days, we know how much confusion there was. Michael Wolff would sit in the White House lobby," Allen said. "Everyone comes and goes through there. And if you're sitting there waiting for an appointment, you can catch up with a lot of people. Michael Wolff would get dope from people walking through, and then sometimes they would walk across the park and meet him at the Hay Adams Hotel."

While Bannon says he still supports the president and called Mr. Trump a "great man" on his radio show Wednesday night, in Allen's view "this is a divorce."

"This is a severing of the ties. The White House knew this book would probably be bad, but they had no idea Steve Bannon would say the things that he does. But … Steve Bannon has a comeback plan," Allen said, referring to Bannon's efforts recently to travel around the country and build his base.

"Where Steve Bannon was probably kidding himself was, he also told friends, that if the president ran again, Bannon would like to run the campaign. Well, good luck with that. Hard to see Steve Bannon back in Trump Tower," Allen said.