Steny Hoyer, the majority leader in the House of Representatives, told Fox News on Saturday that he hoped to "have a plan we can put forward" by the end of the weekend.
The rescue plan for troubled financial institutions, proposed by the US administration, has proved a hard sell, both to Democrats and members of the Republican party of George Bush, the US president.
John Boehner, the Republican minority leader of the House of Representatives, was less optimistic that a deal was close.
"We had, I'm going to guess, 3,500 calls this week about this particular issue. I've had 95 calls in support of it if that gives you any indication"
Tennessee Republican senator
"There are a lot of issues still on the table. While I think there's goodwill between both chambers and both parties in terms of trying to come to an agreement, there's a lot of conversation yet to occur," he said during an afternoon break in talks.
Republicans in the House of Representatives have put forward a rival plan calling for an expanded insurance system financed by banks to rescue individual home mortgages, so that taxpayers do not have to fund the bail-out.
Boehner said the alternative proposal "reflects the core free-market, pro-taxpayer principles of our party".
Several polls this week showed many Americans were sceptical of the package backed by Bush.
In one poll, 55 per cent of people said they did not believe the government should be responsible for bailing out private companies with taxpayers' money, even if the collapse could damage the economy.
Bob Corker, a Republican senator for Tennessee, who serves on the Senate Banking Committee, said congressmen were encountering extraordinary voter anger.
Referring to his own Senate office, he said, "We had, I'm going to guess, 3,500 calls this week about this particular issue. I've had 95 calls in support of it if that gives you any indication."
The entire House of Representatives and one-third of the Senate are facing re-election on November 4.
Bush told citizens in his weekly radio address that he understood taxpayer frustration for being asked "to pay for mistakes on Wall Street".
|Bush told Americans that he understood their frustration [AFP]
Seeking to persuade Americans to support the deal, he said: "The failure of the financial system would mean financial hardship for many of you.
"The result would be less economic growth and more American jobs lost. And that would put our economy on the path toward a deep and painful recession."
The plan originally put forward by Henry Paulson, the US treasury secretary, was criticised for failing to provide enough oversight.
That plan would have largely awarded Paulson powers to use the multi-billion dollar sum of taxpayers' money to buy up bad debt, such as mortgages, held by any financial institution for two years.
Both Democrats and Republicans have expressed disquiet that so much money from taxpayers would go to private companies, but Bush assured voters in his radio address that over time the value of those assets would rise again.
"This means that the government will be able to recoup much, if not all, of the original expenditure," he said.
Other governments have watched the protracted talks closely, concerned the financial turmoil could spread.
Wen Jiabao, China's prime minister, on Saturday called for international co-operation to resolve the crisis, saying Beijing's contribution would be to maintain its own economic stability.
"All countries must strengthen their co-operation. They must all take proactive measures to deal with the crisis," he said at a meeting organised by the World Economic Forum in the north Chinese city of Tianjin.
Gordon Brown, the UK's prime minister, on Friday assured Bush that "Britain supports the financial plan - and whatever the details of it, it's the right thing to do to take us through these difficult circumstances".