US Treasury Secretary Timothy Geithner has said there will be no deal to avert a "fiscal cliff" unless Republicans accept a tax hike for the wealthy.
But House Speaker John Boehner has dismissed a 10-year plan, which aims to raise $1.6tn (£1tn) 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 1 January could trigger a recession.
Mr 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 Mr Boehner, negotiating for the Republicans who control the House of Representatives, said talks with the administration had so far gone "almost nowhere".
Talk show entrenchment
Mr Geithner and Mr 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," Mr Geithner told CNN's State of the Union.
He called on Republicans to make a counter-offer to the Obama administration's plan.
But Mr Boehner said he was "flabbergasted" by Mr 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 $1.6tn of new money?" Mr Boehner asked Fox News Sunday. "He'd spend it."
Mr Boehner says asking the top 2% of US taxpayers to pay more would deal a "crippling blow" to a fragile economy, and has criticised criticised 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 $600bn (£347bn) out of the economy.
The measures were partly put in place within a 2011 deal to curb the yawning US budget deficit.