Former Trump campaign manager Corey Lewandowski insisted to CBS News that he has "nothing to hide" from special counsel Robert Mueller's team in the ongoing investigation into Russian election meddling and any ties to the Trump campaign. Lewandowski and former deputy Trump campaign manager David Bossie appeared Tuesday on CBSN's "Red & Blue" to promote their new book, "Let Trump Be Trump."

Lewandowski said he thought his political career was over after he was fired from the Trump campaign after 18 months on June 20, 2016, but realized later it could be "the greatest thing that ever happened."

"And guess what happened? Maybe it was the greatest thing that ever happened because all of the things that took place basically took place after I left," Lewandowski said. "And if Bob Mueller or anybody else wants to talk, I'd be happy to because if anybody colluded or cooperated with Russia to impact the outcome of the election, I want that person to go to jail for the rest of their lives," Lewandowski said.

"I don't know what Bob Mueller is going to do but what I do know is this," Lewandowski soon after added. "I have nothing to hide, Dave has nothing to hide. And if we can shed light on anything, great."

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The two distanced themselves and the core of the campaign from former campaign aide George Papadopoulos and former national security adviser Michael Flynn, both of whom have pleaded guilty to lying to the FBI. Bossie said he and the president have "great respect" for the work of the FBI, but also emphasized there needs to be accountability in the FBI, after FBI agent Peter Strzok, who was key in the Clinton email investigation, was removed from Mueller's team for allegedly sending anti-Trump texts. Mr. Trump has claimed the reputation of the FBI is "in tatters."

"It undermines the American people's belief in the justice system, that justice will be served equally. And so that's why in our book we talk about Hillary quite a bit," Bossie said.

Bossie also addressed the "Access Hollywood" tape, after a New York Times report that Mr. Trump questioned the authenticity of the video in which he seemingly describes grabbing women, after apologizing for the incident shortly before the election.

"But it is, it's, the president steps off of the bus," Bossie said. "The president's voice is with Billy Bush." Bossie said.

"My position is, we wouldn't even be talking about this if in the last several weeks, men around the country, whether it's Hollywood or here in New York or in Washington, whether it's in politics or in the media, weren't just wrapped up in just a sea of activity by them that is now trying to wash over on the president," Bossie said. "I think it's unfair to him. But it is the day and age we live in. We say we wouldn't even be talking about this, we could get to the important issues of the day. But what is going on in the world today ... it's an important conversation to have."

Lewandowski, once Trump's campaign manager, is now president and CEO of Lewandowski Strategic Advisors, while Bossie, former deputy campaign manager, is the president of Citizens United.

The book's title comes from a central strategy Lewandowski wrote on a white board in the early days of the campaign, a message that remained there throughout his tenure as campaign manager -- "Let Trump be Trump."

The book, released Tuesday by Hachette Book Group and obtained by CBS News, has some revealing passages of what it's like to work for Mr. Trump. In their work, Bossie and Lewandowski describe a man who can be difficult to work for -- bombastic, full of expletive rants and curious demands.

"Sooner or later, everybody who works for Donald Trump will see a side of him that makes you wonder why you took a job with him in the first place," the book says. "His wrath is never intended as any personal offense, but sometimes it can be hard not to take it that way. The mode that he switches into when things aren't going his way can feel like an all-out assault; it'd break most hardened men and women into little pieces."

Mr. Trump sometimes made unusual demands of his staffers, according to the former Trump aides. "Let Trump Be Trump" describes how then-candidate Trump would have Hope Hicks, now the White House communications director, steam his clothes on the campaign plane -- while Mr. Trump was wearing them.

"Get the machine!" he'd yell. And Hope would take out the steamer and start steaming Mr. Trump's suit, while he was wearing it! She'd steam the jacket first and then sit in a chair in front of him and steam his pants. One time, Hope forgot to bring the steamer on the jet. "I don't think we have time, sir," she said when he yelled for the machine. 'We'll just get you pressed at the hotel." But Mr. Trump insisted. When Hope finally admitted she'd forgotten the steamer, he blew his top. "Goddammit, Hope! How the hell could you forget the machine?"

Corey Lewandowski, center left, and David Bossie, center right, wait to greet President Donald Trump during the 139th Easter Egg Roll on the South Lawn of the White House in Washington, D.C. on Mon., April 17, 2017. The White House said 21,000 people are expected to attend the annual tradition of rolling colored eggs down the White House lawn that was started by President Rutherford B. Hayes in 1878. The Washington Post

In the book, Bossie recalls Mr. Trump telling key associates the day before Election Day, "First of all, I'm going to win. And second, if the Republican Party is going to run away from me, then I will take you all down with me. But I'm not going to lose."

That threat to take down the GOP still holds true, Bossie and Lewandowski said in a recent interview for POLITICO's Off Message podcast. They didn't say in the interview whether Mr. Trump will stay a member of the Republican Party.

"I think the president very much respects the Republican Party," Lewandowski said on the podcast. "He is very engaged with the Republican National Committee and helps them raise a lot of money and understands that having Republicans controlling Congress is a fundamentally different thing than having Democrats."

Bossie, in his interview with CBSN, expressed frustration that the president hasn't had as much success as he's used to having.

"Promises made and promises kept are a theme in our book," Bossie told CBSN. "And you know, we're frustrated for the president that he's not had the kind of success he's used to because he's a guy who wants to move very quickly, and he wants to move, he wants success, and he wants the American people to see that he can get things done, that Washington isn't broken anymore."

"The American people are frustrated and I'm frustrated along with them," Bossie added.