The Gallup poll indicates 54% believe it's not up to the federal government to provide healthcare insurance coverage.
The Affordable Care Act passed in March 2010.
And in June, the Supreme Court upheld most of the president's initiative including allowing patients with pre-existing conditions access to insurance.
It also allows young adults to stay on their parents' insurance plans.
President Obama's election victory neutralized efforts by Republicans to overturn it.
It's the first time in 12 years the Gallup poll trend has shown a majority of Americans feel the government shouldn't be responsible for providing healthcare coverage.