This is a partial transcript of "The Big Story With John Gibson," June 8, 2006, that has been edited for clarity.

(BEGIN VIDEO CLIP)

REP. DENNIS HASTERT, R-ILL.: This is a major victory for our troops and the Iraqi people. A victory for the War on Terror and certainly our America families. Al-Zarqawi was certainly a murderer and a known beheader of innocent civilians and, while important, we know that this victory does not yet signal the end of our duty. We must continue to find these victories.

(END VIDEO CLIP)

JOHN GIBSON, HOST: The death of Zarqawi is great news, but the war isn't over in Iraq yet. This one victory has revived the debate over whether we should bring our troops home. House Majority Whip Roy Blunt of Missouri joins us now.

So Mr. Blunt, John Kerry said Thursday, I mean almost the second Zarqawi's death was announced, the American troops have done their job, let's bring them home. What do you think?

ROY BLUNT, R-MO.: You know, I really can't imagine that John Kerry or anybody else would say that. In fact, I was just in Baghdad and Irbil, both, we met with Kurdish leaders as well as leaders of the new government and asked the question over and over again what would happen if we left in the next 90 or 180 days? The answer was disaster or chaos or something like that every time.

We can leave Iraq eventually. I think we can leave probably sooner now than we might have thought we could yesterday. But not in the immediate future and not before we have helped this broad-based government establish itself.

The other big thing that happened Wednesday, John, of course, was finally having the government fully in place, the first permanent, elected, broad-based government in the history of the country. In the long run, that will actually be the bigger of the two events, but eliminating the strategic leader of the terrorists helps a lot in the short run.

GIBSON: Mr. Blunt, we are led to believe and we are led to think here that this guy, this one individual was tremendously important to the insurgency, that you kill one guy and you have done tremendous damage to the opposition to the Iraqi government, the U.S. forces, the coalition, etc. Do you believe thats true?

BLUNT: I believe we have done damage. I think it will turn out we didn't do tremendous damage with this one event. Now we have taken in the short-term the strategic leader out with some of the people closest to him. But a car bomb went off Thursday in Baghdad and other things will continue to happen.

Standing up the army, standing up the police force, we're well on the way with the army. We are making good progress with the police force, though it could be better. Those are the things that still have to happen. We have to get rid of terrorism, disband these free-roaming militias. A lot of that doesn't have anything to do with al-Zarqawi. But it's a great part of people getting more confidence in this new government and the government able to deal with what governments are supposed to do. And its an important thing. There is no doubt about that. But we shouldn't overestimate what this one incident means.

GIBSON: Well, you know, a lot of people are saying, look, you know, there is going to be violence. There will be continued violence in Iraq. There are still militias going after each other. There is still sectarian violence but this one guy was responsible for so much beheading, for starting the sectarian fight over the last few months, blowing up the golden dome mosque, the incident only Sunday of 21 Shiite school kids being hauled off a bus and killed. So when he makes a difference, a small difference or a big difference?

BLUNT: Well, he makes a difference. You know it's hard to know what the balance is. Not to make too much of this or too little of it. This is a vicious guy. He is a murderer of innocent people. He is a beheader of innocent people. He has been called and calls himself the Prince of Al Qaeda. Having him off the scene makes a difference but it is not as important as moving forward with the other things that this government now has to do but the government is now in place to do that and so, again, I want to say that that's an equally important part of yesterday's story. And we had good visits with people who were opposed to the United States and coalition forces being in Iraq, who now want us to leave but they don't want us to leave too quickly. They want to be sure that the future of Iraq and the rights of all Iraqis are guaranteed as much as possible before we go ahead and do what we want to do next which is come home.

GIBSON: House Majority Whip Roy Blunt of Missouri. Congressman, thanks very much.

BLUNT: Thank you, John.

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