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Democrats and Republicans elevated their political brinkmanship Sunday on fiscal negotiations in Washington, with Treasury Secretary Timothy Geithner challenging Republicans to improve on his offer -- which Republicans dismissed as “non-serious” and an attempt to undermine negotiations.

Geithner, now President Obama’s chief negotiator with congressional Republicans, told “Fox News Sunday” the White House plan has “balance” and “detail” but he’s willing to hear suggested improvements.

“But what we cannot do is figure out what works for them,” said Geithner, who appeared on all five major TV talk shows. “The ball really is with them now.”

House Speaker John Boehner, appearing later on Fox,  called the offer “non-serious.”

The Ohio congressman also said he was “just flabbergasted” when Geithner presented the plan last week.

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"I looked at him and I said, `You can't be serious,'" Boehner said.

Should the White House and Congress fail to reach a deal, a $500 billion mix of tax hikes and austere cutbacks on federal spending will kick in January 1.

The tax cuts are a holdover from the George W. Bush administration. And the spending cuts are part of a pact between Democrats and Republican after they failed to reach a more measured agreement on how to reduce the county’s estimated $16 trillion debt. The cuts would amount to an estimated $1.2 trillion over the next 10 years.

Republicans are being asked to accept tax increases to generate revenue,  to cut the deficit, while Democrats are being asked to cut government spending, particularly entitlement programs such as Medicare and Social Security, to reduce the deficit.

South Carolina Republican Sen. Lindsey Graham said on CBS’ “Face the Nation” the country will go over the so-called “fiscal cliff” next month should the parties fail to reach a deal.

“It’s pretty clear to me they’ve made a political calculation,” he said. “This offer doesn’t remotely deal with entitlement reform in a way to save Medicare and Medicaid and Social Security from imminent bankruptcy.”

The president’s plan essentially calls for $1.6 trillion in tax increases, $600 billion in savings from changes to mandatory spending programs, including Medicare, and $200 billion in spending.

Geithner told ABC that Democrats might be willing to make deeper cuts but Republicans “need to tell us what these things are.”

He also said his party realizes Republicans are having a difficult time garnering support for tax increases to generate revenue.

Boehner, the chief negotiator for congressional Republicans, scoffs at the idea of $1.6 trillion in additional tax revenue – roughly double what was previously suggested.

“What do you think would happen if we gave the president $1.6 trillion of new money? “He’d spend it,” said Boehner, who wants to close tax loopholes to generate revenue.

The president’s plan also includes new stimulus spending and gives him the ability to raise the debt ceiling without congressional approval.

Geithner told Fox that Republicans “are in kind of a tough position,” and that Democrats might need to give them more time to reach consensus on a plan.

“But what we cannot do is figure out what works for them," he said.

Geithner said the country could go over the so-called “fiscal cliff” by next month and that it could be “very damaging” to most Americans.

Boehner agreed that no deal would hurt the economy but said, “We are not going to kick this can down the road.”

The Associated Press contributed to this report.