More than 43 percent of those respondents had a negative view of the ACA, while just 24 percent had a positive view. The rest had no opinion.
Even people who were affected by a Obamacare provision that predated the October launch of the ACA exchanges selling insurance were, more often than not, negative about the law. Those provisions include allowing adults under age 26 to remain on their parents' health plans.
More than 40 percent of people affected by an Obamacare provision by the fall of 2013 had a negative view of the law, versus 34 percent who had a positive views. The rest had no opinion.
"It is clear that support for the ACA is relatively weak among all the groups that we examined ... who stand to benefit directly from the provisions of the ACA that are being implemented," wrote the authors of the survey.
That "suggests that public education and outreach efforts are falling well short of reaching and informing the ACA target population who stand to benefit from the coverage provisions," they added.
(Read more: Find uninsured? Forget the ER. Ask the tax man )
"Large percentages of those in fair or poor health, those with lower incomes, the uninsured, racial/ethnic minorities and the young have no opinions one way or the other about the law," the authors wrote. They noted that about 40 percent of both Hispanics and of nonwhite Hispanics had no opinion on the law.
"Understanding and addressing the lack of support" among those groups "will be essential to increasing ACA engagement and achieving the increases in coverage sought under the law," the authors wrote.