“I don’t think it was a slam-dunk,” said Dr. Emanuel, now a vice provost at the University of Pennsylvania and a regular contributor to The New York Times’s Op-Ed page. “The president did take very seriously his reputation for following what he said, so he was very reluctant to change his opinion unless he was very convinced.”

Health insurers also insisted on a mandate, as did the Democrats who controlled Congress. In July 2009, Mr. Obama told CBS News that he was “now in favor of some sort of individual mandate as long as there’s a hardship exemption” for people who truly could not afford to buy insurance.

While the White House may have been prepared for the public unhappiness over the provision, it appears to have been caught off guard by the constitutional challenge — in part because Obama advisers regarded the mandate as a conservative notion. The idea gained currency in the early 1990s, when some Republicans proposed their own version of an “individual mandate” as an alternative to the “employer mandate” in President Bill Clinton’s health plan.

Polls show that the individual mandate is unpopular. The Kaiser Family Foundation, which tracks public opinion on the health measure, reported in March that 74 percent of Americans would keep, rather than repeal, the law’s provision barring insurers from discriminating against people with pre-existing conditions. But only 27 percent would keep the mandate. (A CNN poll released Monday found that 52 percent supported the mandate, up from 44 percent in June, though unlike Kaiser, CNN did not explain that failure to comply would result in a fine.)

The Obama administration insists that if the mandate falls, so does the provision on pre-existing conditions. “The mandate,” said Jonathan Gruber, a health economist at the Massachusetts Institute of Technology who has advised the administration, “is the spinach you need to get the chocolate you want.”

Chris Jennings, a former health policy adviser to Mr. Clinton, makes much the same point. “Health reform without an individual requirement,” Mr. Jennings says, “is like driving a train without tracks; you can still move, but you can’t get to your coverage destination and it will be a rougher and far more costly trip.”

But not all economists agree. Some say the government has other ways to make sure that enough healthy people buy insurance and offset the cost of the sick. One option is “auto enrollment,” in which the government would automatically enroll citizens in insurance plans, but give them the chance to opt out. Mr. Starr, the Princeton professor, who helped draft the Clinton health bill, proposes a system of penalties and incentives to get healthy people to enroll. For instance, people could be given a choice: Sign up now, or wait another five years.