As Republicans prepare to cut trillions of dollars in taxes, they are grasping for ways to keep down costs. There are the typical conservative ideas for doing so, like cuts to health care programs, and the inventive ones, like changing how the budget is measured in the first place.

And then there is an unorthodox option Republicans on Capitol Hill and in the Trump administration are quietly considering: a tax increase on the rich.

The idea is one of many tax changes Republicans are floating. Lawmakers and lobbyists expect the party’s anti-tax antibodies to kick in and eventually block it. But even the possibility of raising taxes on high-income Americans has stirred a debate among Republicans about the party’s relationship with the richest Americans as their base of support increasingly comes from the working class.

“You’ve got these two conflicting streams of thought within the Republican Party,” said Dave Kautter, a Treasury official under the first Trump administration. “There’s ‘Let’s raise the rate so we can provide relief for lower- and middle-income people who are now part of our coalition,’ versus the traditional few that say, ‘The top rate should be as low as we can get it.’”

At issue is the marginal tax rate for Americans in the highest income bracket, a group that is largely made up of the top 1 percent of earners. Under the income tax system, Americans pay a higher rate for every dollar they make above increasing thresholds.

In their last major tax cut, in 2017, Republicans lowered marginal tax rates across income levels, including the top rate, which dropped to 37 percent from 39.6 percent. Like many of the other tax cuts Republicans passed that year, the 37 percent rate is set to expire at the end of the year if Congress does not pass another law renewing it.