Still, Mrs. Boxer said, Why not clear things up? “I said to Chairman Dodd, I have an idea that we should put together a very simple bill, an amendment to the bill that basically says what we know is true, that all financial companies put into receivership under this title shall be liquidated. No company is going to be kept afloat. All funds expended will be repaid to the taxpayers by the financial sector through assessments or the sale of the assets of the company.”

Image Senator Richard Shelby, a Republican, opposes the industry-financed fund outlined in the bill. Credit... Amanda Lucidon for The New York Times

In a provision titled, “Liquidation required,” Mrs. Boxer’s amendment states: “All financial companies put into receivership under this title shall be liquidated. No taxpayer funds shall be used to prevent the liquidation of any financial company under this title. All funds expended in the liquidation of a financial company under this title shall be recovered from the disposition of assets of such financial company, or shall be the responsibility of the financial sector, through assessments.”

Her amendment also stresses that taxpayers will not pay for shutting down failed companies. “Taxpayers shall bear no losses from the exercise of any authority under this title,” it states. “All funds expended in the liquidation of a financial company under this title shall be the responsibility of the financial sector, through assessments.”

No votes were expected on amendments to the legislation until sometime next week. With the Kentucky Derby taking place in Louisville this weekend, Mr. McConnell, in particular, has reason to want to head home from Washington.

Debate on the legislation moved forward after Republicans said on Wednesday that they would no longer block the Democrats from bringing the bill to the floor.

The floor fight is expected to last at least two weeks. Republicans control enough votes to filibuster the measure and, if they remain united, could block it from being adopted.

As the debate began, Senator Richard C. Shelby of Alabama, the senior Republican on the Banking Committee, said that he would work aggressively to force changes to the legislation.