It has happened before: In the 1990s, insurers hoped that by using health-maintenance organizations to move their coverage away from expensive doctors and hospitals, they could control health costs while creating an incentive for providers to lower their prices. What they created instead was a popular rebellion, with customers balking at the HMO plans and complaining loudly to Congress about it.

Some analysts see a similar climate brewing now.

“People don’t like to hear ‘no,’ and this is saying ‘no,’ ” said Austin Frakt, a health policy economist at Boston University.

That’s clear from the Kaiser Family Foundation’s latest tracking poll on the health care law. Among those the foundation surveyed, 51 percent said they’d prefer a broader network and higher premiums, compared with just 37 percent who preferred “a more limited range of doctors and hospitals” in exchange for lower premiums. And most of the 37 percent changed their minds once they were reminded that a plan with “a more limited range of doctors and hospitals” might mean the same thing as “you would not be able to visit the doctors and hospitals you usually use.”