House Speaker Newt Gingrich proposed Sunday that Americans with overdue taxes be given a one-year amnesty to pay up without penalties. It’s an idea that could bring in billions of dollars in extra revenue as Congress and the White House struggle to balance the budget, he said.

Gingrich, R-Ga., said the proposal, already tried by several states, would give people a one-time opportunity to “pay up their back taxes to clear the board, and then we would have stiffer penalties if they didn’t take advantage of the amnesty.”

That would increase revenues by several billion dollars and “allow us to have an even deeper tax cut for the honest taxpayers in America,” Gingrich said on “Fox News Sunday.”

In the past week Gingrich has tried to reassert leadership on the tax issue, which is central to the Republican agenda, urging elimination of capital gains and estate taxes. Conservatives criticized him earlier for suggesting that tax cuts could be put off until after a budget deal is struck with the administration.