WASHINGTON — The Bush administration and Congress anxiously revived negotiations Friday on a $700 billion financial bailout, one day after the largest bank collapse in U.S. history provided a brutal reminder of the risks of failure. Democrats talked optimistically of agreement by the end of the weekend.

"I'm convinced that by Sunday we will have an agreement that people can understand on this bill," predicted Massachusetts Rep. Barney Frank, a key Democrat in eight days of up-and-down talks designed to stave off an economic disaster.

House Speaker Nancy Pelosi added that "progress is being made," although the day came and went without senior lawmakers from both parties sitting down together.

Neither she nor Frank divulged details at a late-afternoon news conference in the Capitol, though there was word of one fresh Democratic concession.

Pelosi told fellow Democrats during a closed-door meeting that the idea of letting judges rewrite mortgages to help bankrupt homeowners avoid foreclosure won't be a part of the emergency legislation. That provision, pushed by several Democrats, would be a deal-breaker for Republicans whose votes are needed to pass the measure, she said, according to lawmakers at the meeting.

Democrats and Bush administration officials also said they were willing to include House Republicans' idea of having the government insure distressed mortgages — but only as an option, rather than a replacement for the administration's more sweeping approach.

Democratic and Republican staff aides met into the night on Capitol Hill. They were going line by line through legislative proposals in an attempt to clear the way for lawmakers to bargain over the weekend even as presidential contenders John McCain and Barack Obama agreed during their presidential debate Friday night that Congress must act soon.

Asked directly whether he intends to vote for a rescue plan taking shape in Congress, McCain said, "I hope so. ... sure."

"We haven't seen the language yet," Obama said. "I do think there is constructive work being done."

Meanwhile, new details emerged of a remarkably tumultuous White House meeting on Thursday. With the session breaking up in disarray, according to two participants, President Bush issued an appeal, saying, "Can't we just all go out and say things are OK?" The group around the table, congressional leaders as well as McCain and Obama, spurned the presidential request for a publicly united front.