In 2011, Oregon Gov. John Kitzhaber faced a vexing problem: The state had a $2 billion hole in its Medicaid budget and no good way to fill it.

He could cut doctors' pay by 40 percent, but that might lead to them quitting Medicaid altogether. He could drop patients or benefits, but that would only compound costs in the long run. A former emergency room doctor, Kitzhaber remembers culling the Medicaid rolls in the 1980s, when he served as a state senator.

"When I went back home, and went back to the emergency department, I saw a couple of people who came in who lost coverage under that decision," he said. "One of them was a guy who had had a massive stroke. These people don't disappear."