This is a rush transcript from "Special Report with Bret Baier," June 27, 2018. This copy may not be in its final form and may be updated.

BRET BAIER, FOX NEWS HOST: John Roberts, live on the North Lawn. John -- thanks.

Let's get some analysis now from the outside adviser to President Trump for judicial nominations. Leonard Leo joins tonight. Leonard -- thanks for being here.

LEONARD LEO, TRUMP OUTSIDE ADVISER FOR JUDICIAL NOMINATIONS: Good to be here.

BAIER: First, put this in perspective about how big a deal this opening -- not just an opening, this opening -- is.

LEO: Sure. Justice Kennedy has been on the courts for over 30 years and he's played an enormously important role in helping to fashion so many different areas of our jurisprudence from gun rights to freedom of speech, separation of powers, federalism. It's a big deal.

BAIER: The process being kind of whispers that the Neil Gorsuch blueprint is basically what is going to move forward.

LEO: Yes. The president had enormous success in nominating Neil Gorsuch to the court. And I think that's the kind of process that you'll see going forward -- another nominee like him.

BAIER: Is the sense -- you heard the Senate Majority Leader, that this is going to happen quickly? Is there a timeline on this?

LEO: Usually it takes the White House about two or three weeks to get a nomination out and then normally it takes about 70 to 100 days for the Senate to confirm. So the leader's right, you are looking at the fall. And you could have somebody seated just before the beginning of the October term of the quarter just after it starts.

BAIER: What about the Democrats including the Senate Minority Leader who are out there saying this can't happen? It needs to wait until after the election.

LEO: The president appoints justices to the court. It's one thing to say that, you know, just before a presidential election, we should have a cooling off period. But you have a president. The American people knew he was -- who he was going to nominate because he gave them a list. So we should just move forward.

BAIER: And he is saying that this list is unacceptable. But in reality, because of the vote structure in the Senate, there is really nothing Senate Democrats can do, is there, to stop a nomination from going forward aside from tripping that person up in a hearing?

LEO: If the president nominates someone extraordinary like Neil Gorsuch again, I think it's very hard to stop that kind of a nomination. The American people were widely supportive of Neil Gorsuch and Justice Gorsuch had bipartisan support in the Senate.

BAIER: Ok. Let's talk about a couple of the names that we are hearing about already. John mentioned some of them Judge Brett Kavanaugh, D.C. circuit U.S. Court of Appeals here in Washington.

LEO: Very distinguished service on the federal bench, hundreds of opinions published out of the D.C. circuit, someone who understands that the limits on government power in our constitution are inextricably intertwined with the preservation of freedom in our country.

BAIER: Will he have problems with Democrats?

LEO: Well, as Senator Schumer said, anyone the president nominates will have problems with Democrats. But ultimately I think red state Democrats and moderates in the Senate will understand that someone like Brett Kavanaugh or another Neil Gorsuch type nominee would be quite suitable for our country.

BAIER: He was the top official in the George W. Bush White House.

LEO: Yes.

BAIER: Let's talk about Judge Thomas Hardiman, third circuit, U.S. Court of Appeals chambers in Pittsburgh.

LEO: Judge Hardiman was someone who the president actually interviewed the first time around and again, someone who's been on the bench quite a while, very extensive record, seen lots of cases. Someone again, who understands that it's the job of a judge to interpret the law that is written.

BAIER: Speaking of those laws just recently five-four rulings in which Kennedy was in the majority. You have union dues just out today, Trump travel ban, Abortion language specifics, Texas redistricting, state sales tax, and Ohio voter roll purge just to name a few recently. But he's been a swing vote on a lot of major cases.

Is the fear on the left justified that this means that Roe v. Wade is in jeopardy if one of the 25 gets through the process?

LEO: The left has been using the Roe v. Wade scare tactic since 1982 when Sandra O'Connor was nominated. And over 30 years later nothing's happened to Roe v. Wade.

And the fact of the matter is, we know as much about a number of the justices who -- for example, John Roberts as we knew about Justice Kennedy when he was nominated. So I think their abortion issue is really very much a scare tactic.

This just needs to be about the Constitution more broadly. As you pointed out, Kennedy has been a very important in propelling jurisprudence in lots of different areas of the law and that's what this process should examine.

BAIER: Let's take a listen to Justice Kennedy about the constitution.

(BEGIN VIDEO CLIP)

JUSTICE KENNEDY: It is appropriate to recognize an essential truth. And that is that the Constitution of the United States is the single fact, the single reality, the single idea, the single moral principle that sets the United States apart from other nations now and throughout history. I shall honor the constitution.

(END VIDEO CLIP)

BAIER: Nominated in 1988 by President Reagan. Justice Kennedy made this decision, went and talked to President Trump. Do you know anything about those conversations?

LEO: I understand that it was a very cordial conversation. The president was very impressed with him, his graciousness, the 30 years plus of service he had on the court.

You know, the Trumps and the Kennedys as families have known each other over the years on and off. So I think it was gracious for the Justice to go to the White House and talk directly to the president.

BAIER: Talk about names?

LEO: I don't know if they did. But Justice Kennedy is a very prudent and discreet man. So I suspect that, you know, he understands the role that he plays and the role the president plays.

BAIER: Do you think this will have an effect politically, not where you are, you're looking at the justices and who's going to be nominated, the judges. But as you look at the political landscape that this could have a big impact?

LEO: Any vacancy on the court does. The court these days makes so many important decisions that affect American life. It ought to be an important part of the political process. People ought to think seriously about who they want on the court. And I do suspect it will have some impact in the Senate election process

BAIER: In 2016, all voters -- conservatives and Independents ranked it high for their reason that they chose to vote.

LEO: As they should. As they should.

BAIER: Leonard Leo -- we would love to have you back as this process gets moving.

LEO: Good to see you again.

BAIER: Thank you.

LEO: Thank you -- Bret.

BAIER: Up next a major primary upset for a high ranking congressional Democrat. We'll bring you that.

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