This is a rush transcript from "Your World," January 3, 2018. This copy may not be in its final form and may be updated.

NEIL CAVUTO, "YOUR WORLD" HOST: You know, this whole day seems to have been like this internal war back and forth, the Bannonites, the Trumpites, whether it's the establishment, which is hard to say, because neither of those guys are establishment going against the renegade groups.

Anyway, I can't make it out.

But Newt Gingrich has a long history of this sort of thing and has seen many a president address it. He's the former speaker of the House, you know, multiple bestselling author, his wife a fancy-schmancy ambassador at the Vatican. He joins us from the White House right now.

Newt, good to see you.

NEWT GINGRICH, R-FORMER SPEAKER OF THE HOUSE: Well, it's good to see you.

I'm not sure Callista would quite buy fancy-schmancy, but she's honored to be serving as ambassador to the Vatican.

CAVUTO: That is awesome. I mean, that's quite the honor.

Let me ask you, though, how is this all going down, this Bannon back and forth with the White House, the president and his remarks?

(LAUGHTER)

CAVUTO: It wasn't just a tweet. It was a very clear, delineated statement.

What is going on?

GINGRICH: Well, look, I think, Neil, first of all, Bannon has an exaggerated sense of self-importance, and the news media, of course, builds it up, because it's exactly, in the age of the Kardashians, the kind of nonsense that they love to fill time and space with.

So, they can run around and think about that, as opposed to the largest tax cut in history, or the most deregulation in history, or the best economic growth in more than 10 years.

CAVUTO: But didn't Bannon feed this beat, Newt, by saying this outlandish stuff?

GINGRICH: Well, look, I think that Bannon thinks he's extraordinarily important.

But the fact is, Trump had won the nomination without Bannon. Trump would have won the presidency without Bannon. And Trump has governed without Bannon.

So I think there's an exaggerated sense of who Steve is. And I think, remember, this is a guy who got fired. So you have a guy who has been fired who is trying to claim a bunch of things, which he apparently did not claim at the time.

And I think you have to just say, you know, it's noise. It has nothing to do with -- the things that matter to America and the things that matter to the American people have no relationship to the kind of noise that we're going to spend all day today with.

And luckily for the president, he's really come to distinguish between the things that matter and the things that don't. The meeting this weekend at Camp David matters with the Republican leadership. Steve Bannon saying a bunch of junk doesn't really matter in the long run. It will disappear.

CAVUTO: What are you doing there?

GINGRICH: I'm hanging out with friends, talking to some folks, and trying to be helpful.

CAVUTO: That's power. That's power.

Newt, the one thing I wanted to ask about ahead of this meeting is this concern that there might be a government shutdown. Do you think there will be? And with the January 19 deadline looming here, that on the eve of the one-year anniversary of the president's inauguration, is he worried about that?

GINGRICH: Well, I think he's only worried in the sense that he doesn't think it's good for the country to have a government shutdown.

And the way it's going to be structured, you would be shutting down national security, you would be shutting down law enforcement. A lot of dangerous things would happen.

So, my guess is, they will find a formula, they will find a way to avoid it. And certainly that's the intent, I think, of Speaker Ryan and Majority Leader McConnell and the president, is to find a way to keep moving forward.

CAVUTO: This back and forth on the tax cut thing, too, and Democrats are bemoaning it, but we see more companies sharing the wealth with their workers -- today, it was Southwest and American Airlines joined about eight or nine other companies, more likely to come, who will share some of that bounty.

That goes beyond just the individual tax relief that folks are going to see and see in their paychecks I guess next month. Play out the effect of all of this and the impact this is going to have.

GINGRICH: Oh, I think historians will look back and say that the greatest mistake the Democratic Party made in the first two years of the Trump administration was voting unanimously against the tax cuts.

This means that in states -- in places like Missouri, Indiana, Ohio, North Dakota, where we have Democrats, and West Virginia, they voted against cutting taxes, they voted against people back home, they voted against creating more jobs.

And as it becomes clear that in a lot of these states, 95 or 100 percent of the families are going to get a tax cut, they are going to have to ask themselves, do I really want a senator who wants my money to go to Washington instead of to me? Do I want a senator who voted against creating more jobs?

This bill is going to be the most important single event of the first two years of the Trump administration. I think it's going to lead the Republicans to pick up four to six Senate seats and to keep control of the House. And people will look back and say this was the biggest single mistake the Democrats could have made, to be unanimous.

CAVUTO: You think Republicans are going to pick up Senate seats?

GINGRICH: Absolutely. They will pick up to four to six Senate seats.

CAVUTO: And hang onto the House?

GINGRICH: They will keep the House, plus or minus 10.

CAVUTO: So, there's this crowd that says they're going to lose a lot of seats. You don't see that happening?

GINGRICH: Look, I watched everybody who was wrong in 2015 and 2016 and 2017.

When they collectively come out and say something, I take the opposite position. And it's worked every single year now. All the experts who said that Republicans are in deep trouble, you watch as this tax bill comes in, as people realize how big it is, as jobs get created, as economic growth accelerates.

You're going to have the terrible economic years of Obama and the remarkable growth years of Donald J. Trump. I think the average Americans is going to vote for more jobs, more take-home pay, and a bigger economy. And, therefore, I think we're going to win this fall.

CAVUTO: I don't know how much you dabble in the markets. But a lot of folks who love the president are still saying they're getting concerned about a bull market that is getting a little long in the tooth. It's touching on 25000. It would be the 7,000-point leap since the president was elected, the sixth of his presidency.

Do you?

GINGRICH: Do I what?

CAVUTO: Get nervous.

GINGRICH: Do I worry about it?

I don't know. I mean, my honest is, we have never...

CAVUTO: Oh, I think you know. I think you know exactly.

GINGRICH: Look, we have not had a president like Donald J. Trump since Andrew Jackson in the 1820s.

We have never seen the level of deregulation we're seeing. Now, if you're a person who believes that the regulatory state was creating friction, undermining economic growth, weakening the economy, then the scale of deregulation alone is probably worth a half-point of real economic growth to a full point.

Then you look at the tax cuts, you look at expensing, for example, and the impact, which you know very well, Neil, is going to huge in terms of an invest boom, and you have to say to yourself, when you look at consumer confidence, we could be in the early stages of one of the most -- this could be like 1921-'22.

We could be in the early stages of one of the most remarkable bull markets in American history. I don't know if it's true or not.

CAVUTO: All right.

GINGRICH: I mean, first of all, I'm a historian. I'm not a business adviser.

(LAUGHTER)

CAVUTO: That's a very good answer.

Newt Gingrich, thank you very, very much. Very good seeing you.

GINGRICH: Great to be with you. Thanks.

END

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