“Some differences” remain on the table, Mr. Frank said, but nothing in his choice of words or demeanor suggested that he viewed those differences as unbridgeable. The discussions continue to be based on “the core” of the plan offered by the administration through Treasury Secretary Henry M. Paulson Jr., Mr. Frank said.

The hopeful report from the Democrats came after President Bush appealed for urgent action, and lawmakers in both parties said they would continue to press for a swift deal. But all were wrestling with realities imposed by presidential politics and the Congressional elections, which have led some legislators to see little political benefit in voting for the bailout.

Both parties were still trying to digest the ramifications of a remarkable uprising led by House Republicans, who said on Thursday that they could not support the administration’s plan. The Republicans have challenged the Democrats, who hold a majority in Congress, to approve the package on their own. But Democrats say they need the White House to persuade reluctant Republicans in Mr. Bush’s party to go along.

After Thursday’s high political drama at the White House, Republicans sought to contain the disarray that led House members and Senator John McCain, the party’s presidential nominee, to essentially scuttle the administration’s $700 billion bailout plan. While some Republican senators said they were close to a deal, others insisted it was not so.

Before flying to Mississippi for the first presidential debate, Mr. McCain met on Friday morning at the Capitol with the minority leader, Senator Mitch McConnell, and with House Republican leaders, who then installed Mr. Blunt of Missouri to replace Spencer Bachus of Alabama as their lead negotiator.