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Daniel Webster makes pitch to be next House speaker

This is a rush transcript from "Your World," October 6, 2015. This copy may not be in its final form and may be updated.

NEIL CAVUTO, HOST: We have got Hillary Clinton, who is seizing on this Benghazi thing to her own advantage. And she might have been helped a little bit by a guy who wants to be the next speaker of the House, Kevin McCarthy, who has been arguing that those Benghazi hearings that had been ongoing in the House have actually brought Hillary Clinton's numbers down.

Well, she lifted that in whole, and now she is using it as campaign fodder.

Reaction from Florida Republican Congressman Daniel Webster, who wants to challenge McCarthy for that speakership. The vote is the end of this month, I believe, October 29.

Good to have you back with us, Congressman. How you doing?

REP. DANIEL WEBSTER, R-FLA.: Great to be back. Thanks, Neil.

CAVUTO: Do you think, maybe unintentionally, he just gave Hillary Clinton some wind at her back?

WEBSTER: Well, it probably is unfortunate what happened.

But my problem is not with any of the individuals running for speaker. My problem is with the way the House of Representatives is run. And if we don't get ahold of that, we're not going to solve any problems. We have got to establish a principle-based, member-driven process by which every person gets to be a player.

A few people at the top of the pyramid of power is not what...

(CROSSTALK)

CAVUTO: Well, what does that mean? Obviously, you're not a Tea Partier here. You want to just change the way the system operates.

And a lot of Republicans fear you're not going to give them the advantages, the advantage in the House.

WEBSTER: Oh, they will get the advantage. Every rank-and-file member will have an advantage.

When a few people at the top of the pyramid of power make all the decisions, then we're disadvantaged. When they push everything to the back end of an issue, or whatever it is, when the deadline is coming, that puts the membership at risk.

To me, you take up the most important issues first. I did that in Florida.  And then you push down the pyramid of power, empower each of the members to have an opportunity to be successful. When you do that, that moves away from a power-based system to a principle-based system. That benefits...

CAVUTO: We should explain. We should explain, sir. Not everyone is up on your background. But you were speaker of the Florida House. So, you learned a thing or two about how to work with opposing parties and opposing interests and different personalities.

The rap against Speaker Boehner is that he never quite got that down and there are a lot of sore egos as a result. How can you avoid that? Because they think that you would be no, offense, Boehner-lite.

(LAUGHTER)

WEBSTER: Well, I'm the opposite of that.

I want to have a flattened-out pyramid of power, where every member gets to be a part. And the advantage to that is this. And the telling is in what happens. Our polls are at 11 percent on last Friday. They were that at the 1st of January.

CAVUTO: Whose polls? You are talking about Congress' approval ratings?  

WEBSTER: Congress' polls and their favorability.

CAVUTO: I understand.

WEBSTER: When I was in the state legislature, we had about the same kind of polling, until we took over and we changed everything. We took up the most important issues first. We adjourned on time. We didn't push against any deadlines or any shutdown of government or anything like that. And...

CAVUTO: So, you would never advocate shutting down the government for any reason?

WEBSTER: No, because we're going to take up the issues first.

CAVUTO: OK.

WEBSTER: We're going to get them done first. And it works. And then in the end...

(CROSSTALK)

CAVUTO: So, that is very different than a Jason Chaffetz, who is also running for speaker, the three of you, Kevin McCarthy, yourself and Jason Chaffetz.

He says a little fire and brimstone is needed now and then. You say what?

WEBSTER: Well, here's what I'm telling you.

When you do what I'm just describing, our numbers flipped right side up, 56-27. Name any legislative body in the country that has ever had numbers like that. It works. The people notice. And when you do things right, by principle, the membership is going to be benefited greatly by that.

And you are going to end up producing a product that is of the House, not of a certain group, a small group of people.

CAVUTO: All right.

Congressman, thank you. We will watch very closely towards the end of the month. Good seeing you again.

WEBSTER: Good seeing you. Thanks for letting me be on.

CAVUTO: All right.

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