Sen. Patty Murray Patricia (Patty) Lynn MurrayPoll finds support for independent arbiters resolving 'surprise' medical bills Senate Democrats introduce legislation to probe politicization of pandemic response Trump health officials grilled over reports of politics in COVID-19 response MORE (D-Wash.) on Sunday said Democrats were prepared to allow the expiration of all George W. Bush-era tax rates to take place if Republican lawmakers objected to raising taxes on the wealthiest earners.

“We can't accept an unfair deal that piles on the middle class and tell them they have to support it. We have to make sure that the wealthiest Americans pay their fair share,” said Murray on ABC's “This Week.”

Murray said one option would be to let the lower rates expire across the board and then return to the table next year with new talks on a tax-cut package.

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“So if the Republicans will not agree with that, we will reach a point at the end of this year where all the tax cuts expire and we'll start over next year. And whatever we do will be a tax cut for whatever package we put together. That may be the way to get past this,” said Murray.

The Washington senator is likely to become chairwoman of the Senate Budget Committee, and previously served on the congressional “supercommitee” that failed to finalize a deficit-reduction plan, which will trigger sequestration cuts in January 2013 unless Congress acts to block them.

Economists warn that the tax-rate rises and automatic spending cuts could bring another recession, and both parties have said they hope to avoid the so-called “fiscal cliff.”

“Look, no one wants to go off the fiscal cliff. But a fair deal is absolutely critical here,” said Murray on Sunday.

President Obama and Democrats have called for raising taxes on the wealthy to pay for the deficit-reduction plan, while Republicans want to extend all the Bush-era rates.

The president will meet with lawmakers next week to begin talks on a deal and said he was “encouraged” last week when House Speaker John Boehner John Andrew BoehnerLongtime House parliamentarian to step down Five things we learned from this year's primaries Bad blood between Pelosi, Meadows complicates coronavirus talks MORE (R-Ohio) said Republicans were open to new revenues in any such deal.

Appearing with Murray, Sen. Saxby Chambliss Clarence (Saxby) Saxby ChamblissLobbying world GOP lobbyist tapped for White House legislative affairs The Hill's Morning Report - Gillibrand drops out as number of debaters shrinks MORE (R-Ga.) praised Boehner John Andrew BoehnerLongtime House parliamentarian to step down Five things we learned from this year's primaries Bad blood between Pelosi, Meadows complicates coronavirus talks MORE. “I thought he showed great leadership by saying that revenues need to be on the table,” said Chambliss.

But Chambliss cautioned that new revenues needed to be matched with measures reforming entitlement programs and said the Bowles-Simpson model could provide a template for negotiators.

“Bowles-Simpson said, look, eliminate all these tax credits and tax deductions. You can generate somewhere 1 to 1.2 trillion [dollars] in additional revenue. You can actually lower tax rates by doing that,” said Chambliss.