House Speaker Nancy Pelosi told "GMA" in an interview with Chris Cuomo taped late Thursday that a deal will be concluded.
"It will happen because it has to happen," she said. "I would hope that we could come to agreement in the next 24 hours."
Pelosi added, however, "That's really up to the House Republicans."
House Republicans rebelled against a deal framework for Bush's $700 billion Wall Street bailout Thursday hours after it was announced by Democrats and Republicans.
That pact would have provided an oversight board, some protection for taxpayers, limited compensation for CEOs, and would have the $700 billion doled out in chunks with a possible cut off after $350 billion.
The talks moved to the White House at 4 p.m. with Bush, McCain and Obama and that's where the deal began to unravel. By 10 p.m., talks ceased for the day with no deal -- but plenty of finger pointing.
Democrats blamed McCain's abrupt decision to leave the campaign trail and inject himself in the talks as the big problem, made worse by Bush's invitation to invite Obama to join the negotiations.
"I think Sen. McCain's involvement is sort of a blip," Pelosi told "GMA." "He hasn't been involved in this." The White House meeting, she said, was "disruptive" and time consuming.
The Republicans charged that Obama torpedoed the talks by running the Democratic side of the negotiations, and as a result, "the meeting quickly devolved into a contentious shouting match."
At the heart of the dispute is a refusal by House Republicans to allocate $700 billion of taxpayers' money to bail out Wall Street fat cats.
"There's a lot of people in Congress, even as we speak this morning, who have deep reservations about the structure of the Paulson plan," Shelby told "GMA." He also cited a petition signed by more than 200 economists urging Congress to reject the bailout.
The House GOP has proposed a scaled down plan in which the federal government would insure the assets of troubled firms instead of buying those assets outright.
The House Republicans devised their own plan after deciding Paulson's wasn't going to be able to win enough votes to pass in Congress.
"It was becoming very clear to us that this [administration-backed] bill was not going to pass in the House," said Rep. Paul Ryan, R-Wis. "There was not support among Republicans, and even many Democrats were not going to vote for this bill."
The Republican split is putting pressure on McCain, partly because he initiated the involvement of the presidential candidates, ABC News' chief Washington correspondent told George Stephanopoulos "GMA."
ABC News' Jonathan Karl contributed to this report.