Among Republicans, 48 percent oppose letting states waive protections, while 42 percent support it. Half of independent voters and 52 percent of Democrats also object to the idea.

But backers of the provision say the sickest Americans would still be protected from steeper premiums as long as they do not have a gap in health coverage. And if a person with a pre-existing condition fails to maintain health insurance, supporters note, they could then obtain coverage through a high-risk pool — though experts have questioned the effectiveness of such programs.

A plurality of voters (46 percent) also oppose letting states determine the benefits that insurers must cover in health plans, while 38 percent support that idea. Under the revised health bill, states would be able to apply for a waiver to opt out of certain federal insurance regulations, such as those requiring insurers to cover Obamacare’s “essential health benefits” provision, which includes coverage for hospital visits, prescription drugs and maternity care.