Half of the Americans who remain uninsured several years into Obamacare are eligible for government assistance in buying coverage, a new survey shows.

In less than three weeks, the Obama administration will embark on the third enrollment period under the 2010 Affordable Care Act, where it faces the ongoing challenge of persuading those who have resisted obtaining health coverage to buy it. About 32 million people, or about 11 percent of the U.S. population, are still uninsured.