President George W Bush has said that legislators will "rise to the occasion" and pass the proposed $700bn (£380bn) Wall Street rescue plan.
He said disagreements remained as "the proposal is big and the reason it's big is because it's a big problem".
Senate Majority Leader Harry Reid, a Democrat, said lawmakers would stay in session until a deal was reached.
But rebel Republicans remain unhappy at the plan to buy mortgage-backed assets from US banks.
However there were some positive signs later on Friday, when Democratic House of Representatives Speaker Nancy Pelosi said progress was being made on a financial rescue bill.
She said Congress was "back on track" in its efforts, and that lawmakers would continue to work over the weekend to reach agreement.
And Barney Frank, Massachusetts Democrat Representative and chairman of the House Financial Committee, said: "I am convinced that by Sunday we will have an agreement that people will understand on this, on this Bill".
Speaking earlier in the day Mr Bush said were "disagreements over aspects of a rescue plan but there is no disagreement that something substantial must be done".
Republicans in the House are going to continue, they say, to try to resist this plan
Senator Reid agreed, saying: "We're going to get this done and stay in session as long as it takes to get it done."
Mr Reid was hopeful a bill could be drawn up by midnight in the US on Friday, and voted on either on Sunday or Monday.
He also said that "the insertion of presidential politics has not been helpful, it's been harmful" adding that Republican presidential candidate John McCain had not made his position on the financial rescue package clear.
Mr McCain, who had announced that he not take part in a presidential debate with rival Barack Obama until a bail-out plan was agreed, said on Friday that he would fly to Mississippi for the debate later.
Mr Bush's public backing for a deal did not ease nervousness on Wall Street, with stocks fluctuating throughout the day on small trading volumes.
However the benchmark Dow Jones index closed the day more than 1%, with the S&P 500 and Nasdaq virtually unchanged.
Senators Harry Reid and Chris Dodd lay out their terms
Republican critics of the bail-out plan are worried about both its cost and how it would involve the government in the financial sector.
The BBC's Adam Brookes in Washington predicted a tough day of negotiations ahead.
"Republicans in the House are going to continue, they say, to try to resist this plan," he said.
"They are also trying to convince Senator John McCain, the presidential contender, to jump in their direction."
Instead, the rebels want a government-backed insurance policy to cover the huge amounts of bad debt built up by US banks.
House Republican leader John Boehner said "we need to act quickly and protect the American taxpayer first and foremost".
Democrats meanwhile want to secure limits to payments for executives of failed banks and ensure there is adequate help for struggling US homeowners.
Financial markets are gummed up because banks do not know exactly how much bad debt they hold and are therefore reluctant to lend to businesses, consumers and each other.
The fall-out of this credit crunch continues to have a huge impact:
The United States suffered its largest bank failure yet, when regulators moved in to close down Washington Mutual and then sold it to US rival JP Morgan Chase for $1.9bn
In a co-ordinated move the European Central Bank, the US Federal Reserve, the Bank of England, Bank of Japan and the Swiss National Bank announced new short-term loans to the banking sector worth tens of billions of dollars
Banks continued to cut costs, with UK banking giant HSBC saying it would axe 1,100 jobs
Shares in UK bank Bradford & Bingley fell another 20% to 17 pence before recovering slightly
Talks to agree the huge bail-out of the financial industry ended in a "shouting match" on Thursday.
After several hours of discussions with President Bush, a group of Republican members of Congress blocked the government plan, which would have seen the government buy bad debts from US banks to prevent more of them collapsing.
The intense discussions reportedly saw US Treasury Secretary Henry Paulson literally down on one knee, begging Ms Pelosi to help push through the bail-out package.
However, the agreement unravelled when a group of Republican legislators objected to the principle of the plan.
The talks at the White House, led by Mr Paulson and US President George W Bush, then descended into what one participant described as "a full-throated discussion".
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