President Trump plans to unveil his new tax plan on Wednesday.

Sources tell CNN he may propose slashing the top corporate rate from 35% to 15% -- as he proposed during the campaign.

Such a dramatic change would likely set up a clash with Republican leaders on Capitol Hill.

Here's why: Republican leaders are eager to cut corporate taxes, but for various reasons they don't want to add to the country's debt. And a 15% corporate rate could drive up deficits by a lot.

For example, the Tax Policy Center estimated in November that Trump's 15% proposal, coupled with a repeal of the corporate Alternative Minimum Tax, could reduce revenue by nearly $2.4 trillion in the first decade.

To put that in context, that's about $240 billion a year -- which is almost as much as the $304 billion the government spent last year on income security programs such as food stamps, unemployment benefits and child nutrition.

The cost could jump to nearly $4 trillion if Trump also chooses to extend the 15% rate to so-called pass-through businesses, which include everything from small businesses to big law firms and investment partnerships. The owners and shareholders of those businesses pay a top rate of 39.6% today.

Related: Trump relies on magic wand of growth to pay for tax cuts

The price tag could be somewhat less if Trump chose not to repeal the corporate AMT. But if he didn't, that would greatly undercut the value of the rate reduction to 15% for many corporations because they would have a higher tax bill under the AMT, said Roberton Williams of the Tax Policy Center.

The TPC was working off a plan from the Trump campaign that was thin on details. So absent those, it's hard to do a more tailored cost estimate.

But it's very fair to assume the cost of reducing the corporate tax rate will be high.

Administration officials cautioned that nothing is final. And sources told CNN that Wednesday's announcement is not likely to offer much explanation for how tax reductions would be paid for.

Treasury Secretary Steven Mnuchin has said, however, that Trump's tax plan would be paid for through economic growth. Experts throw cold water on that idea, since there is no evidence that tax cuts pay for themselves.

The Wall Street Journal first reported that Trump wants to include a 15% corporate tax rate in Wednesday's announcement.

Senate Finance Chairman Orrin Hatch said that a 15% corporate tax rate would be problematic because it would increase the deficit and run into parliamentary problems if Republicans try to pass their tax bill under a procedure that lets them avoid a filibuster.

"I'd love to do that. [But] I'm not sure we can get them down that low," Hatch said when asked about the proposed rate.

-- CNN's Jeff Zeleny, Jim Acosta and Manu Raju contributed to this report.