“Any reductions we have in upper income taxes will be offset by less deductions so that there will be no absolute tax cut for the upper class,” Mr. Mnuchin said in an interview with CNBC on Wednesday morning. “There will be a big tax cut for the middle class, but any tax cuts we have for the upper class will be offset by less deductions that pay for it.”

That is not what independent analysts concluded after analyzing the tax proposal Mr. Trump made during his campaign, which would reduce the income tax rate on the wealthiest families from its current 39.6 percent to 33 percent.

In that plan, middle-class families would see a 0.8 percent increase in their after-tax income, according to an analysis by the Tax Foundation, while the top 1 percent of taxpayers would see a 10.2 to 16 percent gain. Another group, the Tax Policy Center, calculated middle-class families would get a 1.8 percent boost in after-tax income, while the top 0.1 percent of earners would see a 14 percent gain and a tax cut worth an average of $1.1 million.

But Mr. Mnuchin was talking big: “This will be the largest tax change since Reagan.”