Doctors, for one, say patients’ attitudes are changing. “Because it’s from Dollar 1 to Dollar 2,000, they are being really conscious of how they spend their money,” said Dr. James Applegate, a family physician in Grand Rapids, Mich. For example, patients question the need for annual blood work.

High deductibles also can be daunting. David Welch, a nurse in California whose policy has a $4,000 deductible, said he was surprised to realize he had delayed going to the dermatologist, even though he had a history of skin cancer. Mr. Welch, who has been a supporter of the need to overhaul insurance industry practices for the California Nurses Association union, said he hoped his medical training would help him determine when to go to the doctor. “I underestimated how much that cost would affect my behavior,” he said.

Dr. Rebecca Jaffe, a family practice doctor in Wilmington, Del., said more patients were asking for the generic alternatives to brand-name medicines, because of hefty co-payments. “Now, all of a sudden, they want the generic, when for years, they said they couldn’t take it,” she said.

The insurers, which base what they charge in premiums largely on what they expect to pay out in future claims, say they still expect higher demand for care later this year. “I think there’s a real concern about a bounce-back, a rebound, in utilization,” said Dr. Lonny Reisman, the chief medical officer for Aetna.

Because they say they expect costs to rebound, insurers have not been shy about asking for higher rates. In Oregon, for example, Regence BlueCross BlueShield, a nonprofit insurer that is the state’s largest, is asking for a 22 percent increase for policies sold to individuals. In California, regulators have been resisting requests from insurers to raise rates by double digits.

Some observers wonder if the insurers are simply raising premiums in advance of the full force of the health care law in 2014. The insurers’ recent prosperity — big insurance companies have reported first-quarter earnings that beat analysts expectations by an average of 30 percent — may make it difficult for anyone, politicians and industry executives alike, to argue that the industry has been hurt by the federal health care law. Insurers were able to raise premiums to cover the cost of the law’s early provisions, like insuring adult children up to age 26, and federal and state regulators have largely proved to be accommodating.