Last week’s back-and-forth in the Senate was emblematic of a process that has at times seemed on the brink of anarchy. Lawmakers have missed many deadlines, including the one Mr. Obama set for all five Congressional committees to wrap up work by August. (Only four did.) Even close allies of the White House sometimes questioned its approach.

“It felt like it was getting out of control at the end of July and in the beginning of August,” said John D. Podesta, a former chief of staff to President Bill Clinton who informally advises the Obama White House. “People were getting nervous that it was going every which way.” Mr. Podesta said the president risked “giving too much rope to a Congress that is liked a lot less than he is.”

Image Speaker Nancy Pelosi, second from right, at an event last week for the House health care bill. Credit... Luke Sharrett/The New York Times

Mr. Obama said early on that he would not repeat the mistakes of Mr. Clinton, who wrote his own detailed plan, only to see it fall flat on Capitol Hill. Instead, the president set out broad principles  an approach that the House speaker, Nancy Pelosi of California, acknowledged at a rally last week, when she thanked Mr. Obama for “the intellectual contributions” he had made to the legislation.

The president’s distance caught Congressional Democrats by surprise. It took them months to realize that Mr. Obama would not weigh in on some issues, like the precise shape of a government insurance plan. One House Democrat called it a “a laissez-faire strategy.”

But in an interview in his West Wing office on Friday evening, Mr. Emanuel  joined by other top members of Mr. Obama’s health care team  disputed that characterization. He said the White House had given “leeway to legislators to legislate,” but “not leeway to take a policy off track.”

Mr. Emanuel also said it was no accident that “the basic bones” of the House and Senate legislation were, despite some big differences, quite similar. “While there was a cry for more presidential direction,” he said, “that direction was being provided by the president’s staff.”