To get a waiver, a state would need some other way to cover people with potentially serious medical conditions, ranging from a reinsurance program that helps pay for customers needing very expensive care to a high-risk pool. Such pools existed in 35 states before the Affordable Care Act, but they served only a small fraction of the people who needed coverage and most were underfunded, according to an analysis by the Kaiser Family Foundation.

States could also seek to opt out of a requirement that all insurance plans cover 10 “essential health benefits,” including prescription drugs, maternity care, mental health care and addiction treatment. By allowing insurers to cover less, the change could bring down premium prices, but also leave people without access to services that hundreds of thousands have received under the Affordable Care Act, including treatment for opioid addiction.

It is hard to predict how broadly the waivers would affect the millions of people with pre-existing conditions. Many people do have lapses in coverage between jobs or at other times, and they could be priced out of any program a state set up. Healthy people would most likely gravitate to plans that offered minimal coverage, which could greatly increase costs for those who need more comprehensive care.

Governors have so far remained quiet about whether they would seek waivers, but for many people who rely on the individual insurance market, these provisions hark back to a time when insurers scrutinized the health of all individuals before they could sign up. In some states, policies were available with riders that excluded a given condition. Insurers could also just charge those with medical conditions much higher prices.

Larisa Thomason, of New Market, Ala., remembers the day 15 years ago when her husband got a letter from Humana informing him that his policy would not cover any cancer care because a preventive colonoscopy had turned up several benign polyps. Likewise, an insurer in Wisconsin refused to cover any treatment related to Alice Thompson’s reproductive system, starting in 2003, because a doctor had written in her medical record that she should have a hysterectomy to eliminate painful menstrual periods.

“Had I gotten ovarian or uterine cancer, I wouldn’t have been covered,” said Ms. Thompson, 62, of South Milwaukee. “For 10 years, I was living under this uncertainty of ‘what if.’”