But House Speaker John Boehner has dismissed a 10-year plan, which aims to raise $1.6 trillion through tax rises and spending cuts, as “silliness”.
The two men met on Thursday as time runs out to broker a deal.
Economists warn planned tax rises and spending cuts due to take effect on January 1st could trigger a recession.
Timothy Geithner, negotiating for the White House, has drafted a plan that includes more spending to help for the unemployed and struggling homeowners, as well as cuts in Medicare and other benefits.
On Friday President Barack Obama warned of a “Scrooge Christmas” if soon-to-expire tax breaks for households earning below $250,000 were not renewed as part of the deal to avert the fiscal cliff.
But John Boehner, negotiating for the Republicans who control the House of Representatives, said talks with the administration had so far gone “almost nowhere”.
Timothy Geithner and John Boehner’s appearances on a number of Sunday television talk shows showed how entrenched their positions were.
“There’s not going to be an agreement without rates going up. There’s not,” Timothy Geithner told CNN’s State of the Union.
He called on Republicans to make a counter-offer to the Obama administration’s plan.
But John Boehner said he was “flabbergasted” by Timothy Geithner’s proposals – which he said asked Congress to give up its power to set the nation’s debt limit.
“What do you think would happen if we gave the president $1.6 trillion of new money?” John Boehner asked Fox News Sunday.
“He’d spend it.”
John Boehner says asking the top 2% of US taxpayers to pay more would deal a “crippling blow” to a fragile economy, and has criticized the Obama administration’s proposed spending cuts as inadequate.
The White House has suggested it would not support any deal that did not increase tax rates on the wealthiest.
The fiscal cliff would suck about $600 billion out of the economy.
The measures were partly put in place within a 2011 deal to curb the yawning US budget deficit.
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