WASHINGTON — The middle class will see a big tax cut, but the wealthy will not. American businesses will pay much lower taxes, and as a consequence bring back billions of dollars from overseas. All this will create sustained growth of 3 to 4 percent a year and prevent the budget deficit from exploding.

That is the economic future described on Wednesday by the people President-elect Donald J. Trump’s has chosen to lead the Treasury and Commerce Departments, Steven Mnuchin and Wilbur Ross.

But in making those bold promises, the two men have contradicted some of Mr. Trump’s campaign pledges, promised economic growth targets that will be difficult to achieve given modern demographics, and committed to plans that even sympathetic analysts project will vastly widen the budget deficit.

The comments shed light on how two men tapped as top economic policy makers in the Trump administration view their job ahead — but also expose what will be challenging about getting campaign goals accomplished.