BIRMINGHAM, Ala.—Ernest Maiden was dumbfounded to learn that he falls through the cracks of the health-care law because in a typical week he earns about $200 from the Happiness and Hair Beauty and Barber Salon.

Like millions of other Americans caught in a mismatch of state and federal rules, the 57-year-old hair stylist doesn't make enough money to qualify for federal subsidies to buy health insurance. If he earned another $1,300 a year, the government would pay the full cost. Instead, coverage would cost about what he earns.

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