"There is the widespread feeling that we are making good progress," said Senator Mitch McConnell, leader of the Republican Senate minority.
"The goal would be to vote on an agreement on Monday.
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Democrat lawmaker Steny Hoyer, majority leader in the House of Representatives, also voiced optimism a plan could be agreed to buy up toxic assets from banks and stave off the gravest financial crisis since the Great Depression.
"Hopefully by the end of ... tomorrow, we'll have a plan we can put forward, Hoyer told Fox News, after lawmakers debated the proposal into the early hours of Saturday.
President George W. Bush expressed confidence a deal could be forged and sought to calm the wrath of many Americans who view the bailout as a huge handout for private companies while leaving ordinary people in the lurch.
"I know many of you listening th