Even members of her own family take advantage of a flawed system, in her view, by getting Medicaid. “They don’t work because they don’t want to, and they get free health insurance.” She said. “What the heck? If my husband and I, who grew up with relatively middle-class backgrounds in wealthy states, know people that mooch off the system in our immediate families, imagine what it’s like elsewhere.”

Ms. DiCola’s father, a solo-practice lawyer, is also a Trump supporter, but she is a liberal Democrat and uneasily aware of the anger and frustration that unsubsidized Obamacare customers are feeling — so much so that at first, she worried about sharing her story with The New York Times and “being dragged through the mud on some 24-hour news channel” for being on Medicaid.

She described her state’s plan to impose work requirements on Medicaid recipients as “poor-shaming.” Her friends show more empathy, she said. When she needed a root canal and crown last year and Medicaid would not have paid for it (dental care is one area that Medicaid does not cover comprehensively, or sometimes at all), she posted about it on Facebook and her friends jumped in to help.

Ms. DiCola doesn’t expect to need much health care this year — just a physical and a new pair of glasses, which Medicaid will cover, she said. Still, she added, “You never know what could come up — my appendix could decide to burst tomorrow.” In which case, Medicaid would cover the emergency room visit, surgery and hospital stay, a huge relief to Ms. DiCola, who became so anxious as Republicans in Congress tried to repeal the Affordable Care Act last summer that she felt physically ill.

Ms. Hurd has had no such peace of mind. A burst appendix would likely cost at least her individual deductible of $6,300.

By late January, Ms. Hurd had begun to believe that the only way for her family to have any access to health care was to drop their insurance and save the $928 a month to spend on care when they need it. Harry’s recent illness had rattled her, and Matt wanted to see a chiropractor for back pain that was threatening his ability to work.

“We can’t afford to both treat his back issues and pay for insurance,” she said one morning. She was crying, and it was time to go to work.