Gary Cohn was in some ways an unlikely choice for Donald Trump's White House. He is a Democratic Wall Street veteran serving a Republican president who cast himself as the champion of "forgotten people" battered by economic change.

But Cohn, 57, jumped at the chance to leave a top job at Goldman Sachs and become director of the National Economic Council at the White House. His introduction to government has been relentlessly turbulent, marked by staff shakeups, a damaging defeat on health-care policy, and a president whose popularity sags under the weight of self-generated controversy. After Trump failed to unequivocally denounce white supremacists and neo-Nazis this summer, Cohn himself felt compelled to speak out.

But the moment Cohn has waited for is here. He and his boss, along with Republican congressional leaders, have begun the effort to enact their tax-cut plan despite tepid public support, fierce Democratic resistance and uncertain GOP unity.

Cohn sat down to discuss the plan in a classroom at American University, where he gained his first exposure to financial markets at a student. What follows is a condensed, edited transcript of their conversation.

CNBC's John Harwood: So, we're at American University, where you went to school. Tell me what you learned about yourself.

Cohn: I learned a lot about being confident, about learning how to succeed.

I did get introduced to the financial markets while I was in college. And I think I learned also how to sort of filter out all of the nonrational, or nonsensible, noise and sort of concentrate on what matters, and that's really what markets are about. Separate the rational from the irrational; separate what matters now to what doesn't matter now.

Harwood: I think most people looking from the outside see more irrational stuff happening in this White House than in any White House that they've seen.

Cohn: I'm involved in the economic side of the White House. On the economic side, I think the reality is pretty strong for what's going on in this White House. You know, you can look at the jobs data. You know, we had 4.1 percent unemployment last month, which is a 16-year low. We've had two-consecutive quarters of over 3 percent GDP growth with hurricanes in the last quarter. You look at what the stock market's telling you about people committing capital and willing to invest in our economy. Things are really strong.

Harwood: All those strengths kind of undercut the argument that 'Oh, we have to do tax reform right now,' don't they?

Cohn: We have not had wage growth in this country. So, we've got a lot of Americans finding work, but they're finding work at stagnant wages. Really to continue going on with this recovery, this long recovery, is we have to find a way to really drive wage growth. What our tax plan is really aimed at doing is creating wage growth.

Harwood: What were the one or two most important principles that drove what you did?

Cohn: The president had two really important principles. Number one is we have to deliver middle-class tax cuts to the hardworking families in this country. Number two, our corporate tax system just is not competitive with the rest of the world. We have to create a corporate tax rate, and along with that a pass-through tax rate, that makes us competitive with the rest of the world so we can attract businesses back to the United States.

Harwood: Let me suggest an alternative principle. Look at the components of the plan: big corporate reductions, big pass-through reductions for business, much more tax cuts for businesses than for individuals. You've got the elimination of the estate tax, you've got the preservation of the step-up basis, you've got the elimination of the alternative minimum tax. What you have is a bunch of people, including you, including the president, who think 'What I do is good for the economy, therefore, taxing the things that I do less will be good for the economy and good for other people' instead of giving direct benefits to those people. Because middle-class people in this tax cut do not get very much in direct benefit.

Cohn: I just completely disagree with you.

Harwood: Look at the numbers.

Cohn: I've done nothing but look at the numbers for the last 90 days.

Harwood: If you look at Joint Tax, $1 trillion in net cuts for business, $200 billion through the estate tax, and $300 billion for individuals. So, four times as much in business tax cuts and estate tax as for individuals.

Cohn: Yup. But, John, if you look at what we're doing for middle-class taxpayers, the reality is kind of simple. The median-income family in the United States, the family that earns about $60,000 in the United States, the Speaker [Paul Ryan] talked about them getting a $1,182 tax cut. That family is now paying a marginal tax rate of less than 1 percent. They're paying less than $500 of total taxes in the system. So a $60,000 earner, family of four, is paying less than $500. We have cut their taxes significantly. You can't go much further in the tax system.

Harwood: You're saying you can't give middle-class taxpayers more of a tax break than you've done?

Cohn: Unless you want to start going negative tax rates and go into the negative world. So, when people score this, you're scoring against the bound of zero.

Harwood: You have a tax bill that takes away deductions for high medical expenses; that preserves carried interest — I know they're working on that; that takes away deductions for grad school tuition breaks; that takes away an adoption credit. And on a percentage basis, people in the top 1 percent get twice as much of a reduction in their effective tax rate as everyone else.

Cohn: Yeah, look, first of all, we're not done. The only thing you have to work on now is the House blueprint. We're going to get a Senate plan later this week. Remember, the big thing we're trying to do is we're trying to solve for middle income, hardworking families.

Harwood: The companies that benefit from pass-through rates are high income because if they were middle income they'd be paying at the 25 percent rate already. The vast majority of those benefits go to wealthy businesses.

Cohn: You've got to wait till the whole plan is done and see where we finally end up, and see what the plan comes out. Everything in our tax plan is meant to encourage investment.

Harwood: You're not saying, as you did a few weeks ago, that the wealthy do not get a tax cut under your plan?

Cohn: No. I'm saying there's unique situations to everyone out there. Everyone has their own story. It's not our intention to give the wealthy a tax cut.

Harwood: But they're getting one.

Cohn: I don't believe that we've set out to create a tax cut for the wealthy. If someone's getting a tax cut, I'm not upset that they're getting a tax cut. I'm really not upset.

Harwood: Your old colleague, Steve Bannon, says, 'Ask him why they didn't design a tax plan focused on average Trump voters.' And when I talked to Larry Summers, who's your predecessor at the NEC, also Treasury secretary, he said, 'Look, they're doing what their money wants.'

Cohn: They're entitled to their opinions.

Harwood: Why are they wrong?

Cohn: We have achieved our objectives. We are delivering a middle income tax cut …

Harwood: Small.

Cohn: We are lowering corporate taxes to make ourselves competitive with the world.

Harwood: Big.

Cohn: Yeah.

Harwood: If you look at the center of gravity of the economics profession, what they will say is that the deficit will go up more than you guys say, growth will increase less than you guys say, and that workers will get less than you guys are projecting.

Cohn: We vehemently don't agree. When you take a corporate tax rate at 35 percent and move it to 20 percent, and you see what's happened over the last two decades to businesses migrating out of the United States, migrating profits out of the United States, migrating domicile out of the United States, and hiring workers out of the United States, it's hard for me to not imagine that they're not going to bring businesses back to the United States.

We create wage inflation, which means the workers get paid more; the workers have more disposable income, the workers spend more. And we see the whole trickle-down through the economy, and that's good for the economy.

Harwood: Another thing Larry Summers told me: 'The country wants to spend more on defense. We've got a whole lot of baby boomers retiring. We are going to need more money for government and not less.' The Penn-Wharton model — run by a former Bush administration economist, not a Democrat — says that this plan by 2040 will lose $4 trillion. During that time, the number of people on Social Security is going to go from 45 million to 72 million. How in the world does that make sense?

Cohn: We firmly believe that we are creating a model that creates economic growth in this country.

Harwood: But you know no tax cut's ever paid for itself.

Cohn: The years that we increased deficit are years when our economy is slowing down. We continue to borrow more and more money. So, the number one thing we can do for the United States citizens is to grow the economy. This tax plan is meant to grow the economy.

Harwood: Are you thinking that you'll deal with that Social Security/Medicare/baby boomer retirement issue later by entitlement reform that reduces benefits?

Cohn: Look, the president on the economic front laid out three core principles. Number one was reg reform, number two was taxes and number three was infrastructure. We're working our way methodically through reg reform, taxes and infrastructure. I think when he gets done with those, I think welfare is going to come up. That's our near-term economic agenda right now.

Read more from the Gary Cohn Speakeasy interview:

... on keeping companies in America.

... on repealing the estate tax.

... on Cohn's plan after tax reform.

... on comparing Goldman Sachs and the White House.