“It’s not in dispute that many Americans’ lives are being disrupted in an important way by this law,” said Representative Scott Rigell, Republican of Virginia. “Is it also true that some Americans’ lives have gotten better? Yes, and to not acknowledge that is to deny reality.”

The health care law, he said, needs “more of a course change than a course reversal.”

But even with the glimmers of good news, the law faces enormous challenges. A poll conducted last month and released Wednesday by the Harvard University Institute of Politics found that a solid majority of Americans between the ages of 18 and 29 — a constituency crucial to the success of the health law — disapproved of the law and among the 22 percent of that age group who did not have insurance, only 29 percent said they would definitely or probably enroll.

The Obama administration was counting on seven million enrollees by the end of the first enrollment period in March, a number that was supposed to ensure a safe mix of sick, older people and young, healthy ones. Because of problems with the federal insurance exchange and the negative publicity around the rollout, the total is likely to be well short of that.

Representative Dave Camp, Republican of Michigan and chairman of the Ways and Means Committee, said the administration needed to be enrolling close to 100,000 people a day to meet its target. Because state-based websites are doing better, other calculations put the necessary number closer to 40,000 a day, but few are suggesting the goal of seven million is within reach.

“A year from now, if you’ve got too many people to kick it down and not enough to make it work, clearly, there has to be a Plan B,” said Representative Michael Burgess, Republican of Texas and an ardent critic of the law.

White House officials said such prognostication was premature. The experience of Massachusetts under Gov. Mitt Romney showed that most people, especially young people, acted only when they approached a deadline, and with the federal law, the deadline to have insurance or pay a penalty is months away. The officials argue that the total number of people who sign up for insurance is less important than the composition of those enrolled, and they pointed to state figures to suggest the mix was good. More than one-quarter of enrollees in Kentucky are 35 and younger. In California, 22.5 percent are between 18 and 34.

Because insurers on the exchanges cannot discriminate by pre-existing conditions, applications do not ask questions that would indicate the health of enrollees, said Cori Uccello, senior health fellow at the American Academy of Actuaries. So while insurers will know the ages of their new customers, they won’t know their health status until they start filing claims next year.