Republican leader John Boehner said Sunday he was "flabbergasted" by Treasury secretary Tim Geithner plan to save the nation from the fiscal cliff, in the latest show of brinkmanship over a deal to avert the year end budget crises.

His statement came as Washington leaders took to the airwaves amid an escalation in the clash over how to avert the automatic triggering of massive spending cuts and the expiration of across-the-board tax cuts.

Geithner went on a media blitz Sunday to defend president Barack Obama's position over the fiscal cliff. With less than a month to go, Geithner said he could not promise Congress would find a solution. If the tax rates expire and cuts are imposed as they stand, the Congressional Budget Office calculates the US will be plunged back into recession and unemployment will spike to 9.1%.

"That's a decision that lies in the hands of the Republicans that are now opposing an increase in tax rates" for the wealthiest Americans, Geithner told Fox News Sunday.

Geithner told CBS's Face the Nation: "Just remember to extend those tax cuts costs $1tn dollars over 10 years. There is no way we can get back to a balanced plan that put us back on the path to living within our means, protects Medicare, invests in things we need, if you extend those tax cuts."

Boehner, speaker of the House of Representatives, renewed his stand against increased tax rates for the rich. "Here's the problem," Boehner told Fox. "When you go and increase rates, you make it more difficult for our economy to grow." Boehner said if Republicans agreed to give Obama a proposed $1.6tn in new tax revenue, "He's going to spend it," not reduce the deficit.

Last week, Obama said he believed the two sides would reach an agreement before Christmas. "We're nowhere," Boehner said Sunday. The president's advisers have set out a plan that calls for the expiration of tax cuts for those earning over $250,000 as part of a plan to raise $1.6tn more in tax revenues over the next 10 years. In exchange, Obama agreed to $400bn in savings from entitlement programmes over the next 10 years but pushed those talks into next year with no guarantees.

On CBS, Republican senator Lindsey Graham slammed Obama's plans to tackle the debt crisis by imposing higher taxes on the most wealthy. He said Obama's plans failed to address entitlement reform – cuts in social security and Medicare benefits. Graham championed a plan first put forward by failed presidential candidate Mitt Romney to cap the size of deductions that the rich can take.

"If you raise tax rates you get $400bn in revenue and you hurt job creation. If you limit reductions to about $40,000-$50,000 per person, you protect the middle class and you get about $800bn in revenue," he said. "And 100% of Americans are going to lose everything we know as America if we don't fix entitlements. We are becoming Greece because of out-of-control entitlements."

"I think we are going over the cliff. It's pretty clear to me they have made a political calculation," said Graham.

Geithner said he still believed a deal was possible and that the "political theatre" could be a sign of progress. "I actually think that we're gonna get there," he said on ABC's This Week. "I think we're actually making a little bit of progress, but we're still some distance apart."

The row comes amid signs that political deadlock is harming the US economy. Business leaders have said they are holding back on hiring as they deal with the uncertainty created by the fiscal cliff. On Friday, the US releases its latest non-farm payroll figures, the key monthly jobs report which may give a fuller picture of the fiscal cliff's true impact.