“That balloon is going to get popped pretty quick,” Priebus said of hedge fund excitement during an interview with ABC News' “This Week” on Sunday. “So just stay tuned on that. So, I mean, carried interest is on the table, and the president wants to get rid of carried interest. So that balloon’s not going to stay inflated very long. I can assure you of that.”

When hedge fund managers take a cut of profits they earn for their clients, it's called carried interest and is taxed at the long-term capital gains rate of 20 percent instead of the usual income tax rate, which can be as high as 39.6 percent. On the campaign trail, Trump said he wants carried interest to be taxed as income, as hedge fund managers are “getting away with murder” under the current setup.

Trump's tax plan has been criticized for costing too much and benefiting the wealthy instead of the working-class voters key to his electoral victory. Many Republicans have privately questioned his proposal to lower the corporate tax rate to 15 percent, well below where GOP lawmakers had been targeting.

Trump said in an interview with CBS News's “Face the Nation” that aired Sunday that he would pay for the tax cut with money collected from reciprocal taxes, more favorable trade deals and an improved GDP. When pressed, the president said he is “not going to touch” Medicare funding, which some Republicans have suggested cutting.

Senate Minority Leader Charles E. Schumer (D-N.Y.) blasted the Trump tax plan, noting that 90 percent of the benefits proposed go toward top income earners while the vast majority of workers would take a hit because of the proposed elimination of deductions for state and local taxes. He said the tax plan is close to traditional conservative Republican orthodoxy, showing the president is “not governing from the middle; he's governing from the hard right.”

“That is not how Donald Trump campaigned,” Schumer said on "Fox News Sunday," pointing to the tax plan as one of many campaign promises that Trump has abandoned.

Priebus would not say whether the president would be willing to raise taxes on the country's wealthiest people because he did not want to “get ahead of where we're at on the negotiation side.” But he said that even though the top tax rate would be lowered, the wealthiest individuals would no longer be able to take certain deductions — so he doesn't expect a major reduction in Trump's personal taxes.