WHEN Karen Pineman of Manhattan received notice that her longtime health insurance policy didn’t comply with the Affordable Care Act’s requirements, she gamely set about shopping for a new policy through the public marketplace. After all, she’d supported President Obama and the act as a matter of principle.

Ms. Pineman, who is self-employed, accepted that she’d have to pay higher premiums for a plan with a narrower provider network and no out-of-network coverage. She accepted that she’d have to pay out of pocket to see her primary care physician, who didn’t participate. She even accepted having co-pays of nearly $1,800 to have a cast put on her ankle in an emergency room after she broke it while playing tennis.