'FOX NEWS SUNDAY' HOST CHRIS WALLACE: We want to check in today to discuss the latest developments both overseas and on the home front with Senator Lindsey Graham (search), Republican of South Carolina, and a member of the Armed Services and Judiciary Committees, and he joins us from Clemson, South Carolina. Senator, welcome back to "FOX News Sunday."

SEN. LINDSEY GRAHAM, R-S.C.: Good morning, Chris.

WALLACE: Let's start with Iraq (search) and comments that you made in it a hearing last June to Secretary of Defense Rumsfeld. Let's take a look.


GRAHAM: And I'm here to tell you, sir, in the most patriotic state I can imagine, people are beginning to question. And I don't think it's a blip on the radar screen. I think we have a chronic problem on our hands.


WALLACE: Senator, it's two months later. You've been talking to the people of your home state of South Carolina during this August recess. What are they saying now about Iraq?

GRAHAM: Well, nobody wants to withdraw, but people are concerned. It's gone on longer than we thought. The violence is larger than we thought it would be. People are worried about our troops over in Iraq.

And the problem is that the central message has to be that Iraq is the central front on the War on Terror and the chief of staff statement that we may be there four years -- we need to hear more of that, because the worst case scenario is not staying four years. The worst case scenario is leaving a dysfunctional, repressive government behind that becomes part of the problem in the War on Terror and not the solution.

So people don't want to leave, but I'm counseling patience. We've got to get it right. And get it right is having a constitution that empowers women, doesn't repress women, that allows the Kurds to live safely in Iraq and takes care of the Sunni minority by letting them share in the bounty of the country. And that's all going to unfold here pretty soon.

WALLACE: Do they think and do you think at this point that this administration has a strategy for victory?

GRAHAM: The president did a very good job in his radio address. When he spoke to the troops in North Carolina, that was good. We need more of that. The truth is that the international community has taken a pass on this war in Iraq. The international footprint will be smaller by the end of the year than it was after the Iraqis voted. The purple finger moment was a high moment for all of us. We're very proud.

But we need to constantly stress to the American public that our security is tied to a successful outcome in Iraq, and if Iraq dissolves into a state of anarchy, and if women are repressed by a constitution that's repressive, if the Kurds separate creating a problem for Turkey, if the Sunnis are not well taken care of in the constitution, then we've created a major problem for ourselves. And we've got to tie our security to a successful outcome in Iraq.

WALLACE: Senator, let me ask you about the constitution, because there have been some reports from some Kurds (search) and from some Sunnis that the U.S. Ambassador to Iraq, Mr. Khalilzad, in his zeal to try to get a deal, has, in fact, backed the Shiite demands that Islam play a greater role.

And there is some concern that this might, in fact, hurt the rights of women, might increase the play of Islam in the government. What do you think about that?

GRAHAM: Well, this ambassador is a very talented man. He helped navigate Afghanistan through this problem. Having an Islamic statement in a constitution that is an Islamic nation doesn't mean that women are going to be repressed. It could mean that.

You've got all kind of combinations in the Mideast. You have some countries like Pakistan where a woman's testimony is half that of a man. For a woman to prove she was raped, she's got to have four male witnesses. All of that derives from a strict interpretation of Islamic law.

You have places like Afghanistan that have a more secular view. This is a major moment in the development of the Mideast. It's a major moment in the Iraqi people's development. And it's a major moment in our national security.

Deadlines are important, Chris, but we need to get this right. We need a constitution in Iraq that allows mothers to have a say about their children. If we fail there, then we've taken a step backwards. We need a constitution in Iraq that gives the Kurds the ability to govern themselves without breaking away from the country.

We need a constitution in Iraq that will take care of the Sunni minority and let them share in the bounty of the country and not isolate them economically. This decision about to be made in Iraq regarding a constitution is hugely important to us.

WALLACE: Senator, you talk about major moments. Let me ask you about another one. The American Automobile Association came out with some figures this week that were jaw-dropping. Let's take a look at them if we can.

The average price of regular gas across the country is now $2.60 a gallon. In your state of South Carolina it's a little better, but not much, $2.47 a gallon. What are people in your state, Senator, saying about that?

GRAHAM: They're very disappointed in their senator not being able to lower their gas prices. I hear it wherever I go. Iraq and gas are the two dominant issues. And I tell folks there are some problems out there in the world we've got to address.

OPEC (search) has reduced production. China is consuming every barrel of oil they can get their hands on because their economy is growing so fast. Refining capacity doesn't exist in had this country. If you had all the gas you needed, you couldn't refine it. So we've got to have a long-term view of this problem.

The energy bill puts on the table billions of dollars to get away from Mideast oil. It allows the development of hydrogen and electric cars. We have to take a long-term view of this. And the problem is not going to get better in the short-term, but it probably is time to have some hearings in Washington and ask the oil companies why it's so high, too.

WALLACE: Well, let me ask you about the oil companies and their role. Let me show you some oil company statements that came out actually at the end of July. Exxon Mobil, second quarter earnings climbed 35 percent. B.P.'s net income, up 29 percent. Shell's profits, up 34 percent. Conoco Phillips, up 51 percent.

Democrats, Senator, are calling for an investigation to see whether any of those companies are gouging the public. First of all, do you think that that's warranted?

GRAHAM: I think it would be good for Congress to look into the price of gas and why it's been where it's at and the likelihood of it getting better in the short-term or the long-term.

The energy bill was a major step forward to make us more independent. But in the short term, yeah, I think hearings would be necessary. I can tell you this. If Republicans were in the minority, we'd be seeing the same things that our Democratic friends are. This is an American problem.

You know, you led in, what's the Republican response in Iraq. It should be an American response in Iraq. We need to get it right in Iraq and it's going to take a while to build a functioning army and a police force. The first Iraqi battalion was given authority over a region in Iraq two weeks ago. Three days later we had to come in and take over because the ministry of defense couldn't pay the cell phone bill or operate the Internet.

The infrastructure to support an army takes a while. The oil problems in this world are going to take a while to solve. We're just going to have to be patient. But hearings would be a good start.

WALLACE: But given these huge profits which we just put up on the screen, how can you justify the energy bill giving billions of dollars in more tax breaks to these big oil companies?

GRAHAM: To get away from Mideast oil. We have more dependency on Mideast oil now than we have since the 1970s. We need to have a strategy of domestic drilling. We should drill in ANWR (search). We need to develop cars that operate on something other than gasoline -- electric cars, hydrogen cars, hybrid cars.

The investments we made in that energy bill over the next 15 years or 20 years will make us more independent, less dependent on Mideast oil and getting away from fossil fuels in general. We need to revitalize our nuclear industry. Twenty percent of the power in this country comes from the nuclear power industry. In France it's 75 percent. We underutilize nuclear power.

So this energy bill is investing in programs to make us independent of Mideast oil, and I think it was money well spent. But the oil companies need to answer for what's going on right now. I'm all for having hearings.

WALLACE: Senator, let's do a lightning round of quick questions and...


WALLACE: ... quick answers. I know you always enjoy this.


WALLACE: The White House has turned over tens of thousands of pages of men's rights and church-state issues.

Senator, do you see any smoking gun there that could derail the Roberts nomination?

GRAHAM: No. I see a conservative lawyer advising a conservative president about conservative policies, and that's what his job was, to give advice to the Ronald Reagan administration who was pursuing conservative policies.

The headline in The Washington Post that this man, John Roberts (search), is bad for women was ridiculous. The case they were talking about was the Ninth Circuit Court -- federal judge in the Ninth Circuit trying to require truck drivers' pay being given to women working in laundries. Who in this country wants to allow federal judges to set prices for the whole nation?

We have laws against sex discrimination, but he rightfully wrote a brief say no federal judge should be able to micro-manage how much people get paid in particular professions. I don't see any bills by Democrats suggesting that's a good idea.

WALLACE: You're a member of the Judiciary Committee. Do you think that Roberts is a shoo-in to get confirmed?

GRAHAM: Nothing's a shoo-in in Washington, including the nationals. But I think he's going to do very well. I think he will acquit himself well. Here's the issue. Can a conservative judicial candidate giving conservative advice be considered in the mainstream?

I think the answer is absolutely yes, because Justice Ginsburg was a liberal giving liberal advice. She was deemed to be qualified. If you use the Ginsburg standard in terms of how you've conducted yourself throughout your legal career, Judge Roberts becomes Justice Roberts.

WALLACE: All right. I'm going to try to impose the lightning round rules on you again, Senator, because we're about to run out of time.


WALLACE: You went on a trip to Alaska this week along with Senators McCain and Clinton, where they said evidence is mounting that global warming is real and that human activity is largely to blame. Senator, do you buy that?

GRAHAM: Human activity is partially to blame. President Bush said that. And after going to Alaska, I'm more convinced than ever the native Alaskans and the first nation people in Canada are experiencing changes that are unbelievable, never been known in history.

I think man is contributing to the problem. But if you don't have a solution involving China and India, you've just crippled our economy. So any global warming solution about CO2 emissions has to include China and India, and we need to revitalize our nuclear industry because that could help the problem, because it's a clean form of energy.

WALLACE: Finally, there continues to be talk about you as a presidential or vice presidential candidate in 2008 or somewhere down the road. I know that General Sherman is not very popular in South Carolina, but are you prepared to make a Shermanesque statement that you have no interest in higher office?

GRAHAM: I don't know who's talking about me doing those two jobs other than you, but I like being the senior senator from South Carolina. We change senators every 50 years. Senator Thurmond was elected in '54. I was born in '55. I'm glad to have the job, and I want to stick around for a while.

WALLACE: Well, I'll make you a deal. We'll continue this conversation for the next 44 years. Thank you, Senator Graham.

GRAHAM: You report. I'll decide.

WALLACE: Absolutely.

GRAHAM: Thank you.

WALLACE: As always, thank you for joining us. Please come back.