Mr. Nance was surprised that the new law would affect his family, since they had been paying for their own insurance for 11 years. His plan carries a deductible of $3,000 and a premium of about $500 a month. He said that he and his wife were in good health and that their coverage had met their needs.

Mr. Nance learned in September that his existing plan would end on Dec. 31 because it did not comply with the new law. His insurer, Anthem BlueCross BlueShield, offered a replacement plan that would cost nearly twice as much and come with an annual deductible of close to $12,000.

“It’s not affordable, and it’s not better than what I had in any way, shape or form,” Mr. Nance said. He said he does not qualify for federal subsidies, and has had difficulty signing onto the online marketplace to evaluate his options. For now, he has purchased a one-year plan through United Healthcare that is similar in price and features to his existing plan.

In Arizona, Ms. Tyrrell is struggling to figure out her options. For years she dealt with annual rate increases and the fear that her coverage would be canceled.