The poll had a deep partisan divide.
Thirty-six percent of Americans approve of the law and 16 percent had no opinion.
Since its passage in 2010, the Affordable Care Act never garnered support of most Americans in surveys conducted by the Times and CBS, pollsters said.
The U.S. Supreme Court hears arguments on the law's constitutionality this week.
A majority of Democrats -- 56 percent -- said they approve of the law while about 75 percent of Republicans said they disapprove, results indicated. Fifty-one percent of independents say they disapprove of it.
Results are based on a nationwide telephone survey of 986 adults conducted Wednesday through Sunday. The margin of error is 3 percentage points.
Celebrity Families of 2014 [PHOTOS]