The amended bill includes an increase in the amount of bank deposits protected by the government's insurance programme.
Earlier, Asian financial markets recorded gains amid renewed hope that the plan to save America's ailing banks would be adopted.
European stock exchanges were mixed at the close, with the London FTSE 100 index of leading shares gaining 1.17 per cent at 4,959.59 points.
In Paris, the CAC 40 index rose 0.56 per cent to 4,054.54 points while in Frankfurt the DAX fell 0.42 per cent to 5,806.33 points.
Bourses steady
In Asia, markets regained some of the ground they lost on the previous day.
Japan's benchmark Nikkei index closed up 0.96% on Wednesday, despite the Bank of Japan's Tankan corporate survey indicating that Japanese business sentiment had turned pessimistic for the first time in five years.
Markets in Hong Kong, Shanghai and Singapore were closed for holidays on Wednesday but share prices in Taiwan, Australia and New Zealand climbed.
But Song Seng Wun, a regional economist with CIMB-GK Research in Singapore, said that a rebound in stock markets was "not really" the best measure of financial health.
Investors were "taking things day by day" and taking their lead from Wall Street, waiting to see whether help was on the way for the US economy, he told Al Jazeera.
Song said that liquidity was still an issue as until there was greater clarity on a financial plan or on the health of the global financial system, financial institutions were essentially "hoarding cash", lending only to their "most trusted friends".
Modified bill
Republican and Democratic leaders in the House of Representatives have expressed hope that the revised bill will be passed on Wednesday.
Republican house members voted against the rescue package on Monday by a more than 2-to-1 margin. A majority of Democrats voted in favour.
Speaking to Al Jazeera on Wednesday, Allister Heath, editor of City AM, a London-based business publication, said: "I think the only good news is that even if the rescue package does not go through, it is not the end of the world.
"All over the world, governments have been taking their own action; banks have been sold and bought, sometimes nationalised. There have also been private-sector solutions.
"Optimism has returned to the trading floors here in London and also on Wall Street, but it is very hard to predict whether a plan will be passed by both houses of the US congress.
"The problem is that the left and the right tend to disagree [on the rescue package] The left think it is bailing out big banks while the right see it as a form of socialism."
Heath said even if the rescue plan goes through, the problem of the credit crunch will not go away.
"It is merely another weapon to tackle the problem," he said.
"Basically, the credit crunch is getting worse; many more banks will have to be rescued and hundreds of billions of bad debt is going to have to be written off.
"Stock markets will continue to fall, property prices will continue to fall. All over the world, consumers and savers will suffer."