The agreement underscored the rising confidence among Democrats and the Obama administration that Senate Republicans could not hold ranks against the bill for much longer, given the high-stakes election year and the widespread public outrage at Wall Street.

Officials from Goldman Sachs, including its chief executive, Lloyd C. Blankfein, are scheduled to testify at a Congressional hearing on Tuesday. Regulators have accused Goldman of fraud, and Democrats plan to spotlight some of Wall Street’s questionable business dealings and explore the company’s role in the financial collapse.

Given the climate, both Republicans and Democrats have said they eventually expect Congress to approve the most sweeping overhaul of the financial regulatory system since the aftermath of the Great Depression, and new rules bringing greater transparency to the trading of derivatives are one of the bill’s more crucial components. But final passage of the measure would come later rather than sooner if Republicans have their way. Senator Richard C. Shelby of Alabama said on Sunday that his party was still prepared to block debate of the bill as he fought for additional changes, including what he described as tight guarantees against future taxpayer bailouts of banks.

Mr. Shelby said that he was hopeful the two sides would reach an agreement but that he thought it unlikely that it would happen before the Monday vote. “Will we get a bill by tomorrow? I doubt it,” Mr. Shelby said on NBC’s “Meet the Press.” But he added, “I think we will get a bill.”

Told that the two sides seemed close, Mr. Shelby said it wasn’t clear. “Inches sometimes are miles,” he said.

Image Senator Richard Shelby, the Republican from Alabama, appeared on “Meet the Press” in Washington on Sunday. Credit... William B. Plowman/Meet the Press, via Associated Press

Mr. Shelby, and the banking committee chairman, Christopher J. Dodd, Democrat of Connecticut, who appeared together on the show, are scheduled to meet Monday afternoon. And some officials held out hope of a last-minute deal to move forward with floor debate.