ANOTHER RUBE SELF-IDENTIFIES: Sorry, We Don’t Take Obamacare.

AMY MOSES and her circle of self-employed small-business owners were supporters of President Obama and the Affordable Care Act. They bought policies on the newly created New York State exchange. But when they called doctors and hospitals in Manhattan to schedule appointments, they were dismayed to be turned away again and again with a common refrain: “We don’t take Obamacare,” the umbrella epithet for the hundreds of plans offered through the president’s signature health legislation.

“Anyone who is on these plans knows it’s a two-tiered system,” said Ms. Moses, describing the emotional sting of those words to a successful entrepreneur.

They were warned.