The following is a transcribed excerpt of "FOX News Sunday," July 3, 2005.

CHRIS WALLACE, FOX NEWS: Well, liberal and conservative groups have already started running ads about the Supreme Court battle even before the president picks a nominee. This, of course, is the first court vacancy since the advent of cable news and the Internet.

And to find out just how fierce the action may get, we turn to the heads of two of the most high-powered interest groups: C. Boyden Gray, who served as White House Council under Bush 41 and now heads the conservative Committee for Justice; and Nan Aron, who counts the defeat of Robert Bork among her biggest victory, she leads the liberal Alliance for Justice. Welcome to both of you.

Welcome to both of you. I think the one thing we can agree on is we all want justice here. Correct?

C. BOYDEN GRAY, CHAIRMAN, COMMITTEE FOR JUSTICE: Yes, sir.

WALLACE: Mr. Gray, before we get to the campaigns that both of you are running, let's talk about the possibility of the nomination of Attorney General Alberto Gonzales. The New York Times reports today that you led a delegation that met late last week with White House Chief of Staff Andrew Card to warn that appointing Gonzales would splinter conservative support.

GRAY: Well, that was news to me. I don't think we discussed any individuals in that meeting, which was about process, not about people. And I would, of course, support Judge Gonzales if he were nominated. So I don't know where the story came from.

WALLACE: Why are, though -- because you may deny the story but there are a lot of social conservatives who have expressed strong opposition to Judge Gonzales. Why?

GRAY: Well, I think they're worried about where he is on abortion and on affirmative action. But I don't think that's going to be determinative. If the president wants to nominate him, he will, and he will be confirmed.

WALLACE: Ms. Aron, would liberals accept Gonzales, who, as a judge on the Texas Supreme Court, did take somewhat moderate stands on abortion and affirmative action, especially knowing that if you beat him, the president's likely to pick an even more conservative person as the next choice?

NAN ARON, PRESIDENT, ALLIANCE FOR JUSTICE: I think it's difficult to say at this point who we would accept or who we would reject. There's much in Gonzales's record that we really don't know much about. We don't really know about his views on a number of issues: choice, civil rights, women's rights, environmental worker protections. It's really up to the Senate to conduct a broad, thorough review so that we can learn who he is and basically what he thinks.

It's interesting to note that at his hearing for court of appeals -- I mean, for attorney general, he was very evasive and refused to answer most of the questions put to him by the committee. So I think the hearing is an opportunity for the American people to come to understand who he is and how he thinks.

WALLACE: All right. You have called for the president to nominate what you called a moderate consensus nominee, such as?

ARON: Oh, we put out a list a couple weeks ago: Judge Prado, a Bush appointee and now a judge on the Fifth Circuit Court of Appeals; a wonderful Republican judge who now sits in the Seventh Circuit, Ann Williams; and several others.

We believe that it's important for the country for President Bush to name a candidate who accepts individual rights, who accepts the progress we've made as a country and will take us forward, not backward, and will make decisions that serve in the interests of all Americans and not just side with special interests.

WALLACE: Mr. Gray, what do you think of those specific recommendations? And what do you think of the general template that Ms. Aron advanced?

GRAY: Well, Ms. Aron has said and said in debates with me, that one of the reasons why they're so interested in this is because since the Republicans control the White House, the House of Representatives and the Senate, the only place to look for the creation of new rights is the courts. And we believe this is the job of the legislature, not the judiciary.

We think that the president should appoint someone who will interpret -- not make up -- the law; that he is entitled to put on the bench someone who is in the mainstream of where Republican presidents have been for 25 years.

Cass Sunstein, who is the leading academic adviser to the Democrats, has said that there is an extraordinary consistency between the judges nominated by and confirmed by Reagan, Bush I and Bush II. And we think that anyone the president picks from the list that we've all seen, fits well, fits that category of exactly where Republican presidents have been for 25 years, and should have no problem getting an up-or-down confirmation.

WALLACE: Let me just follow up with you, Mr. Gray. There's one thing that all of the senators in the preceding segment agreed on is they didn't like the idea of these outside interest groups. It's been reported, Mr. Gray, that conservative groups, not specifically yours, but a group of conservative coalitions, has $20 million to spend on backing whomever the president picks. Why on earth, how on earth, can he spend $20 million on a Supreme Court confirmation battle?

GRAY: Well, I think that's an exaggeration. I don't think they have $20 million. I think it could get up to that. But from my vantage point, what we're trying to do is play defense: simply get on a level playing field or try to get on a level playing field with Nan Aron and with Ralph Neas and People for the American Way who've been at this business now for 20 years.

GRAY: We're sort of newcomers to it,and we're just trying to counterbalance what they're doing, and the money that will be spent, will be spent to counterbalance what they're doing. It's not, it's more of a defensive measure to support the president, not to try to influence how the president makes his own picks.

WALLACE: Is this what this is about, Ms. Aron, the conservatives just trying to have a level playing field?

ARON: Well, I think it's important to emphasize that liberal progressive groups are not spoiling for a fight. We are hoping that President Bush does just what his predecessors in the White House did, which was to reach across the political aisle and select a consensus nominee. After all, that's just what President Clinton did, and both his candidates -- Ruth Bader Ginsburg, Stephen Breyer -- sailed through confirmation.

That's what Gerald Ford did when he selected Justice Stephens, and Stephens was confirmed in 17 days. It's important for President Bush to follow in their footsteps and engage in a consultative process. In fact, Lindsey Graham, who was just on this program right after that deal was signed, not only wrote language in that deal calling for very strong consultation, but he even chided the White House in a statement for failing to consult with the Democrats over the past few years on judicial nominees.

WALLACE: Ms. Aron, during the campaign, the presidential campaign in 2004, the president was asked: Who are your models for the Supreme Court? And he made it very clear. He talked about Antonin Scalia. He talked about Clarence Thomas. Perhaps the two most conservative members of the court.

It was an issue in the campaign. He won the campaign. Isn't he entitled? That's what elections are about.

ARON: Well...

WALLACE: Isn't he entitled to a qualified conservative of his liking?

ARON: That was then. He was running for president, and he was looking for the support and financial resources from the radical right in this country. Of course he'd make a statement like that, but now...

WALLACE: But wait a minute. He got elected president. The voters selected him.

ARON: No, but with the smallest margin of victory of any incumbent president. He is now the president of a huge country representing nearly 300 million people from all walks of life, representing divergent viewpoints. He has this momentous, historic opportunity to unite the country.

WALLACE: Mr. Gray?

GRAY: Well, I think he will pick from one of a number of distinguished appellate judges who have track records, some longer than others. But they got all confirmed by wide margins to the appellate courts. There's no reason to think they shouldn't get the same consideration for the Supreme Court.

I do not think the president's going to go outside the mainstream of where Republican presidents have been, as I've said. And I think that when the public sees who he nominates, they will embrace that person and see that that person is confirmed.

WALLACE: Mr. Gray, one last thing I want to bring up with you. You were the White House counsel to the first President Bush when he chose David Souter, who I think it's fair to say has turned out to be one of the more reliable liberal members in the court. What advice would you give to this White House to make sure that they don't get surprised on this pick?

GRAY: Well, there's no advice for that, because there's no way to guarantee it. I mean, Teddy Roosevelt found that out with Oliver Wendell Holmes. The landscape is littered with surprises. Just remember, though, that when Souter was nominated, he was immediately attacked, and some liberal groups said women will die if he is confirmed.

Well, you can't always tell how these people are going to vote. Judges are independent. The judiciary is independent. That's the way it should be. And there's no guarantee.

WALLACE: Ms. Aron, Mr. Gray, we're going to have to leave it there. We want to thank you both for coming in today.

ARON: Thank you.

WALLACE: And so much for your summer vacations, huh?

ARON: That's right.