The survey by Robert Wood Johnson, Harvard and Kaiser also found that majorities of Americans favor two controversial provisions of Obama's Patient Protection and Affordable Care Act that would extend health coverage to more than 30 million people who currently have no health insurance.

The first provision, which would create state healthcare exchanges, was favored by 55 percent of respondents who said it should be a top priority for their state governors and legislators. Another 31 percent called the exchanges an important but lower priority. Support included clear majorities of Republicans and Democrats.

Additionally, 52 percent of respondents supported the second provision, which would expand the Medicaid program for the poor to nearly all Americans earning up to 133 percent of the poverty line, equaling about $24,000 a year for a family of three. But opinions split sharply along party lines.