In a shift, Mr. Reid told colleagues on Thursday that he was inclined to include a government-run insurance program in the bill that he would take soon to the Senate floor. States would be allowed to opt out if they wanted.

Asked about Mr. Reid’s idea, Ms. Pelosi said, “I don’t think there’s much problem with that.”

Ms. Pelosi said that in shaping the House bill, she was already thinking about “the endgame.” If the two chambers pass disparate bills, as Democrats expect, negotiators from the House and the Senate would try to reconcile the differences.

When it appeared that the Senate bill might not have any government insurance plan, Ms. Pelosi said, it was essential for the House to pass a strong public option, as a counterweight to the Senate. Now, she said, she will consider an alternative favored by some centrist Democrats, who contend that the government plan should not set prices but negotiate payment rates with doctors and hospitals, as private insurers do.

Ms. Pelosi set the health care legislation in its historical context, saying it “sits very comfortably in the path of Social Security and Medicare,” created in 1935 and 1965, respectively.

Mr. Clyburn said the squabbles among Democrats on health care were like the disagreements in the 1960s among civil rights leaders, who had the same goals but sometimes differed on legislative strategy.

The House majority leader, Representative Steny H. Hoyer, Democrat of Maryland, said Friday that the House could take up the health care legislation as soon as Nov. 6 and might meet on Saturday, Nov. 7, to continue work on it.

But Democrats in both chambers have missed many self-imposed deadlines. And many hurdles remain.

House Democratic leaders are still trying to figure out exactly how to limit the use of federal money for abortions. In addition, before taking their bill to the House floor, Democrats need to get a cost estimate from the Congressional Budget Office.