At a White House news conference, Barack Obama said it would be “absurd” to use the borrowing limit as a negotiating chip.
But Republican House Speaker John Boehner said spending cuts should accompany a federal debt ceiling rise.
The US is expected to hit its $16.4 trillion borrowing limit by February unless lawmakers act.
Monday’s press conference came a week before the inauguration ceremony in Washington DC that will begin Barack Obama’s second term.
With an agreement to prevent the so-called fiscal cliff of sharp spending cuts and tax increases barely two weeks old, Barack Obama faces another budget showdown with congressional Republicans.
The Democratic president warned lawmakers: “They will not collect a ransom in exchange for not crashing the economy.”
He demanded that Republicans in charge of the House of Representatives approve a rise in the federal government’s authority to borrow money to pay existing obligations – without seeking policy concessions in return.
The last debt ceiling battle between Congress and Barack Obama ended in July 2011, after bringing the nation close to default and resulting in a credit rating downgrade as well as financial market turmoil.
“The full faith and credit of the United States of America is not a bargaining chip. And they [Republicans] better decide quickly because time is running short,” Barack Obama said.
He said he was happy to engage in debate over US fiscal policy, but only after an increase in the debt limit.
“We are not a deadbeat nation,” he said.
“While I’m willing to compromise and find common ground over how to reduce our deficits, America cannot afford another debate with this Congress about whether or not they should pay the bills they’ve already racked up.”
He added: “What I will not do is to have that negotiation with a gun at the head of the American people.”
Afterwards, John Boehner, leader of the House Republicans, acknowledged the economic risk of failing to raise the debt ceiling. But he indicated the House would attach spending cuts to any measure to raise the federal borrowing authority.
“The American people do not support raising the debt ceiling without reducing government spending at the same time,” he said in a statement.
Speaking on a day marking a month on from the massacre at a Connecticut primary school that shocked the nation, Barack Obama also said he would present proposals for gun control later in the week.
He said stronger background checks, control of high capacity magazine clips, and an assault weapons ban were all measures he believed made sense.
“Will all of them get through this Congress?” he asked.
“I don’t know.”
The National Rifle Association and some lawmakers have suggested that any plan to ban assault weapons would not pass Congress.
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