Senate Republicans might not repeal the estate tax in the pending overhaul of the U.S. tax code and instead could double the exemption for money individuals or families leave to heirs, lawmakers say.

Doing so would be a major backtrack on a promise Republicans have repeated for years. It could also help drain some ammunition from Democrats, who have sought to paint the tax bill as a giveaway for the rich.

“I don’t think there’s the stomach to do a full repeal,” Senate Finance Chairman Orrin G. Hatch said.

The Utah Republican said instead the GOP will aim to try to find a way to “make it less onerous and burdensome.”

That could include doubling the estate exemption, he said. Individuals can currently leave up to $5.5 million and avoid the federal estate tax. For couples, it’s $11 million.