Mr Obama made the remarks as he tried to win public support for his plan on a visit to a toy-maker in Pennsylvania.
But Republican House Speaker John Boehner said talks with the White House had gone “almost nowhere”.
He said President Obama’s plan to raise $1.6tn (£1tn) of revenue over 10 years was not a “serious proposal”.
Planned tax rises and spending cuts due to take effect on 1 January could send the US back into recession, economists warn.
‘Lump of coal’
On Friday, Mr Obama toured the Rodon Group manufacturing facility, where parts for the children’s toy K’nex are made.
The Democratic president said it was the type of company that depended on middle-class customers to buy its goods, adding it would be hurt if ordinary Americans faced a tax rise.
In a speech at the factory, Mr Obama said both parties would have to “get out of our comfort zones” in order to negotiate a deal on the fiscal cliff, and pledged he would be willing to do the same.
He said that if Congress did not extend soon-to-expire tax breaks for the middle-class, it would be like receiving a “lump of coal” at Christmas.
“That’s a Scrooge Christmas,” Mr Obama added.
Tax cuts passed during the presidency of George W Bush are due to expire under the fiscal cliff.
Mr Obama favours extending the break for households earning below $250,000. But he wants taxes to rise for those on income above that sum.
Mr Boehner said that asking the top 2% of US taxpayers to pay more would deal a “crippling blow” to a fragile economy.
He also criticised as inadequate spending cuts that were proposed on Thursday by the Obama administration.
Treasury Secretary Timothy Geithner put forward a plan to congressional leaders that would raise $1.6 trillion in higher taxes over a decade.
The proposal also envisages spending more money to help the unemployed and struggling homeowners.
And it called for savings of as much as $400bn from Medicare and other benefit programmes over 10 years.
Mr Boehner told reporters on Friday: “There’s a stalemate. Let’s not kid ourselves. Right now, we’re almost nowhere.”
Some Republicans have said they would consider increased tax revenue as part of a deal to avoid the fiscal cliff.
But the White House believes that simply ending tax deductions would not address the yawning budget deficit.
White House press secretary Jay Carney has indicated Mr Obama 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.