Skepticism about Obamacare might have moved up from an all-time low in November, but a newly released New York Times/CBS News poll reports widespread disapproval remains among insured and uninsured Americans about the health law.

The poll found 53 percent of the uninsured, who are supposed to gain the most from Obamacare, disapprove of the law, while 51 percent of Americans who have health coverage also disapprove of Obamacare. Overall support for the law edged up from 31 percent in November to 39 percent this month.

More uninsured Americans (37 percent) believe Obamacare will hurt them—citing increased costs as a major reason—than uninsured Americans who believe the law will help them (33 percent).

The latest poll comes as the Obama administration wraps up a media “blitz” to promote the President’s signature health law. That campaign included a White House event pushing mothers to promote Obamacare to adult children and a widely panned tweet by President Obama’s campaign arm, Organizing for Action.

Heritage health scholar Alyene Senger notes that Obamacare’s string of broken promises likely has a huge impact on public perception of the law.

“Americans are discovering that Obamacare is causing them to lose insurance plans they liked and access to doctors whom they trust all while raising premium costs and deductibles,” Senger said. “They’re realizing that what was sold to them as affordable care is actually expensive, government-mandated coverage that doesn’t fit the needs and wants of many Americans.”