Mr. Reid’s version of the bill would also let states opt out of the program.

“We have compromised four times on the public option,” Mr. Brown had said. “There is no more movement on the public option.”

“Many people wanted to do Medicare for all, but that was never in the cards here,” he added. “We have moved three or four or five times on this, and those days are over.”

In the end, the liberals had no choice, and they moved again. But not without winning concessions in return, including an expansion of the ultimate public plan, Medicare. The agreement announced by Mr. Reid calls for allowing people from age 55 to 64 to buy coverage through Medicare beginning in 2011.

While it is not Medicare for all, it is Medicare for more than under current law, and the liberals view it as a major improvement for people nearing retirement, who face some of the biggest obstacles to obtaining insurance and pay some of the highest prices if they get coverage.

At first, those who want to buy in to Medicare coverage will have to pay full cost. But once provisions of the bill take effect that will provide subsidies to moderate-income Americans, those subsidies could be used to buy either private insurance or coverage through Medicare.

That liberal senators in the negotiations were bargaining from a position of strength was largely due to the strategic efforts of Senator Charles E. Schumer, Democrat of New York, who ranks third in the Democratic leadership, and who pressed Mr. Reid to include a public option in the bill.

Mr. Reid, Mr. Schumer and many others realized that further negotiation on a public option was inevitable if they were to have any hope of enacting the health care bill as a whole. The question that arose, as Mr. Reid combined rival versions of the legislation that were developed by two Senate committees, was whether a public option would be in or out of the bill at the start.