For more on the interview with Reid, watch “The Situation Room” at 5 p.m. ET and read CNNPolitics.com

Washington CNN  — 

Harry Reid says Democrats have one reason to support the Iran deal: Dick Cheney.

In an interview with CNN on Tuesday, the Senate Democratic leader said no one with “any degree of intelligence” should agree with the former vice president, who strongly opposes the agreement.

“I’m sorry, I cannot hold back a smile,” Reid said just hours after Cheney delivered a stinging rebuke of the deal. “There are a lot of good reasons for this deal. But the best is that Cheney’s against it. I mean, think about this: The architect of the worst foreign policy decision in the history of America - to invade Iraq. Look what it has done. Why would anyone with any degree of intelligence agree with him?”

The historic nuclear accord is coming to a head this month as Republican leaders in Congress aim to block the deal. He’s working to secure enough Democratic votes to filibuster the GOP effort to scuttle the agreement. But in a speech to the American Enterprise Institute, Cheney tried to keep up the pressure, arguing the “agreement will give Iran the means to launch a nuclear attack on the U.S.” and calling the six-nation deal “madness.”

Reid said such tough rhetoric will only help his cause.

“The best reason to go along with what President Obama wants is the fact that Cheney doesn’t want it.”

Reid and Cheney have a long history of trading barbs with one another – particularly over the war in Iraq and its aftermath. But Reid is now scrambling to lock down enough Democratic support to block a resolution of disapproval on the Iran agreement from landing on Obama’s desk.

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Obama has the necessary support in the Senate to ultimately protect the deal. But Republicans may still get enough support to overcome Democratic objections and send a disapproval resolution to the president’s desk for him to veto. Reid is hoping to block it in the Senate but doesn’t yet know if he will succeed.

“We’ll see what happens,” Reid said.

He plans to discuss the matter at a party lunch Wednesday.

“Right now we know that the deal is not going to go any place because we have more than enough votes to sustain a presidential veto,” he said.

As the Senate reconvened on Tuesday after a five-week recess, Senate Majority Leader Mitch McConnell said every senator should be “entitled” to an up-or-down vote.

Asked about that demand, Reid said: “Well, I have to smile when you say that.”

“To have the Republicans with a straight face, after they have filibustered hundreds and hundreds of times issues that are of immense consequence to our country now come back and say, ‘Well we shouldn’t do it here,’” Reid said. “So this is just, in effect, being kind of a poor loser. Because the fact is that how Leader McConnell can come out there without grimacing when he would say something like that is beyond my ability to comprehend.”

Reid contended that the world will look down on Republicans for voting to block the deal.

But there are several Democrats in both chambers who also oppose the deal. Reid’s successor as Democratic leader, New York Sen. Chuck Schumer, opposes the deal. But Reid dismissed Schumer’s reasons for opposing the deal – including that Iran could create more trouble in the Middle East and could eventually build a nuclear bomb – as “fluff.”

Reid called Schumer a “wonderful human being,” but said that he “has a constituency that is different than a lot of people’s.”

“But there is no alternative. What he talks about is basically fluff,” Reid said. “There is no alternative. What is the alternative? To have us alone? Have the international community walk away? We have negotiated this in good faith. It hasn’t taken months. It’s taken years. Years. This is the diplomatic breakthrough that will go down in history as one of the biggest diplomatic moves in the history of the world.”

Still, Reid didn’t think Schumer’s opposition will hurt his ability to ascend to become the next Democratic leader, when the Nevadan retires at the end of next year. He said he was “confident” Schumer has not been lobbying Democrats to oppose the deal.

“Chuck will be the next leader,” Reid said. “I am confident of that.”