The following is a rush transcript of the June 20, 2010, edition of "Fox News Sunday With Chris Wallace." This copy may not be in its final form and may be updated.

CHRIS WALLACE, ANCHOR: Here's where we stand on day 62 of the oil spill in the gulf. The Coast Guard reports a new containment system is almost at capacity, capturing more than 1 million gallons of oil daily, which many experts believe is still less than half of what's spewing into the gulf.

Drillers are now within 200 feet of finishing a relief well to plug the spill, but that could still take weeks.

And one of B.P.'s partners in the offshore rig, Anadarko Petroleum, blasted B.P. for what it called reckless decisions and actions that led to the explosion.

Joining us now from Louisville, Kentucky to talk about the oil spill and more is Senate Republican leader Mitch McConnell.

Senator, Democrats have launched a new campaign attacking the GOP for a cozy relationship for big oil based on Congressman Joe Barton's apology this week to B.P. Let's watch.


NARRATOR: If Republicans were in charge, this is the guy who'd be overseeing B.P.

JOE BARTON: I apologize.

NARRATOR: He apologized to B.P. and called the recovery fund a tragedy.


WALLACE: Senator, how do you counter the Democrats' argument that Republicans care more about oil companies than they do about the environment?

SENATE REPUBLICAN LEADER MITCH MCCONNELL, R-KY.: Well, of course, that's nonsense. I couldn't disagree with Joe Barton more. B.P. doesn't need an apology. They need to apologize to us, and they certainly need to cover all the costs of the cleanup and the economic damages as well. And they're going — they're going to.

I think it's important to remember the president of the United States, I believe, is the biggest recipient of B.P. political contributions when he ran. So you know, that's nonsense. We want to get it cleaned up.

And I think the administration — you know, the president himself is in charge of developing a contingency plan to deal with oil spills. What happened to it? We know there are skimmers around the world that could be sent here. Where are they? The administration has a role to play in this and they haven't done a very good job so far.

WALLACE: Let me ask about another aspect of this, and that is the fact that White House chief of staff Rahm Emanuel this weekend is mocking Tony Hayward, the head of B.P., for attending a yacht race off England's Isle of Wight, this, of course, at the same time that President Obama and Vice President Bush — rather, Vice President Biden, rather, were playing golf. Do you see any difference?

MCCONNELL: Well, all of these guys could use a better P.R. advisor, but the point is we need to get the oil leak stopped and we need to keep as much of this oil off the shore as we can. And clearly, not enough is being done.

All the local officials down there in the states that — on the gulf are frustrated as they can be. I read a story about Governor Riley of Alabama locating a particular piece of equipment in Bahrain himself, getting it flown over, and then having some bureaucrat tell him it had to go to Louisiana, not Alabama.

You've got shrimpers on shore who want to pitch in and help. Governor Jindal has been frustrated because of difficulty in getting permission to do things that they want to do. Let's concentrate on getting the leak stopped, which is B.P.'s responsibility. We understand that.

Keeping the oil off the shore — the federal government is the lead horse on that. And you know, the president has been advocating expansion of government across the board in virtually every area. If you're going to advocate expansion of the government, then you look not so good when the government you're already in charge of doesn't function very well.

WALLACE: After — I mean, after the president's Oval Office speech this week, you said this, and let's put it up on the screen. "What they're doing here, in effect, is holding the gulf hostage to a national energy tax."

But in his speech, Senator, much to the distress of the left, the fact is the president didn't mention either an energy tax or cap and trade. What do you — would you be willing to accept and not accept in an energy bill? And do you see any flexibility in the fact that the president didn't mention cap and trade?

MCCONNELL: Well, we knew what he was talking about. You know, his chief of staff has famously said a crisis is a terrible thing to waste. They want to seize on this oil spill to pass a national energy tax referred to around Washington as cap and trade.

They never missed an opportunity to seize on a crisis to turn to the far left to-do list. And this has been a big item on the far left to-do list, a national energy tax. Mark my words, that is precisely what they intend to do, seize on the crisis in the gulf to try to pass this.

Dianne Feinstein, one of our more prominent Democratic senators, said cap and trade or a national energy tax doesn't have anything to do with an oil spill in the Gulf. And she was exactly right.

WALLACE: What would you be willing to support in a new energy bill if not cap and trade or an energy tax?

MCCONNELL: Well, the first thing we need to do is to see if we need to pass legislation related to oil spills. I mean, that's the current problem, you know, not climate change or a national energy tax, but the oil spill itself. That's what we ought to be concentrating on.

And it could well be that new legislation would be required related to that — you know, better inspection, prevention in the future, better cleanup technology. That's the kind of thing we ought to be doing and could do on a bipartisan basis.

WALLACE: But are you saying that you oppose any effort to take a look after this oil spill at how we get our energy in general?

MCCONNELL: No, but I certainly oppose a national energy tax. And by the way, there's a bipartisan majority in the Senate in opposition to a national energy tax, to cap and trade. And that is exactly what they're going to try to push, Chris, after the 4th of July. No question about it.

WALLACE: Let's turn to another subject. The Obama administration now confirms what Secretary of State Clinton told a reporter in Ecuador — namely, that the Justice Department is going to file a lawsuit challenging that new Arizona law that cracks down on illegal immigrants.

One, what do you think of that decision? And what do you think of the argument that the administration apparently is going to make that state law — this state law infringes on federal authority when it comes to immigration?

MCCONNELL: Well, here, again, you can understand the frustration of state officials. We just talked about state official frustration over in the gulf. The national government's responsible for trying to get the oil spill — keep the oil off the shore.

Now you've got the national government over on the border with Mexico. We all know that border security is a federal government responsibility. And so out of frustration, the government of Arizona — the people of Arizona have passed legislation in response to that. You can understand their frustration.

I wish the administration would spend more time on border security and less time passing lawsuits against state governments who are frustrated because the federal government isn't doing what it's supposed to.

WALLACE: Do you think they're wrong if they challenge the Arizona law?

MCCONNELL: Well, we'll see what happens in court. You know, to me, it — they ought to be concentrating on securing the border. You know, this whole immigration issue is a federal government responsibility, and they basically have thrown the ball to Arizona by not enforcing the border.

WALLACE: A week from tomorrow, the Senate Judiciary Committee will begin confirmation hearings on the nomination of Elena Kagan to the Supreme Court. Back in April, Senator, I asked you about a possible filibuster, and let's take a look at what you said.


MCCONNELL: It's highly unlikely, however, unless the nominee is an extraordinary individual outside the mainstream with really bizarre views.


WALLACE: Senator, do you see anything in Kagan's record that is outside the mainstream with really bizarre views?

MCCONNELL: Well, we haven't started the hearings yet. The hearings begin June the 28th. We are beginning to get material from the Clinton library.

I think some of her views are quite troubling, at least to me, in the area of political speech and the First Amendment. She has basically argued before the Supreme Court that the government could ban pamphlets. I find that very troubling.

But I think it's entirely too early to determine whether or not this nominee would be subjected to a 60-vote threshold. We know that the president has filibustered Supreme Court nominees. We know the vice president has filibustered Supreme Court nominees. We know Senator Reid has and we know Judiciary Committee Chairman Leahy has.

I have never filibustered a Supreme Court nominee. But it is possible, but entirely too early to know whether that would be appropriate.

WALLACE: But when you say it's still — it's possible, you're saying you're still leaving that option open?

MCCONNELL: Well, the option is open under the Senate procedures. But to predict that that might happen at this stage of the game is entirely premature.

WALLACE: It's been a remarkable week in the U.S. Senate, where some Democrats have joined Republicans to block a new spending bill that would extend unemployment benefits for people who are about to lose them and also provide state aid that would allow workers not to be laid off. Are some Democrats getting religion when it comes to the deficit?

MCCONNELL: It sure seems so. I mean, we passed a $13 trillion cumulative national debt threshold a few weeks ago. And the issue here with regard to this bill to which you referred is paying for it.

Now, we did manage to take out a piece of that bill last Friday and pay for it. That was a doctor reimbursement issue. We paid for it for six months.

What Republicans have been arguing is much of this is worthwhile and should be done, but it ought not to add to the deficit. And now, as you indicate, a growing number of Democrats are showing that kind of concern, and that's why this big Democratic majority in the Senate has not been able to pass this bill. They can't seem to find a way to pay for it.

And they can't resist the temptation to keep kind of adding additional domestic spending programs every opportunity they get. They've got the same temptation over in the House and running in the same difficulty there.

So maybe we've got some born-again concern on the — on the Democratic side, some born-again deficit reduction people on the Democratic side. It would be welcome to see that.

WALLACE: But, Senator, what about the folks who are going to lose their unemployment benefit? What about the state workers who may be laid off? President Obama in his weekend Internet address says Republicans are making life harder for those people.

MCCONNELL: No, his problem is with his own party. Democrats are joining us in saying these are worthwhile things that should be done but they can be paid for and not added to the deficit.

WALLACE: Let me ask you one last question — we have about a minute left — and that is about the 2010 elections. Democrats say in Kentucky with Rand Paul, in Nevada with Sharon Angle, that the Tea Party has pushed the GOP to nominate Senate candidates who are further to the right and therefore are going to be harder to elect come November.

And now you have reports in the state of Illinois that your Senate candidate there, Mark Kirk, the reports are, has inflated his military record and his experience as a teacher. How concerned are you about all three of those candidates?

MCCONNELL: Well, the Democrats, of course, will be desperately trying to tear down and demonize our candidates because they're in deep trouble. The Gallup poll that just came out this week taken by — actually, an NPR poll just came out this week taken by a prominent Democrat and Republican pollster indicated Americans preferred Republicans over Democrats, what's called a party generic ballot question, by eight points.

And the Democrats are very desperate, and they'll be working hard to try to tear down our members. They're in deep trouble and the reason for that is the American people have looked at this administration. They've seen them running banks, insurance companies, car companies, nationalizing the student loan business, taking over health care, running up debts.

America would like to do a mid-course correction. And that's why if the election were held today, Chris, there'd be a lot more Republicans in the House and Senate than there are at the moment.

WALLACE: Senator McConnell, we're going to have to leave it there. We want to thank you so much, as always, for joining us today. Always a pleasure to talk with you, sir.

MCCONNELL: Thank you, Chris.

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