But a CNN/ORC International poll released Monday also indicates that more than a quarter of those who oppose the Affordable Care Act, say they don't support the measure because it doesn't go far enough.
According to the poll, 43 percent of the public says it supports the health care law, a figure that's mostly unchanged in CNN polling since the measure was passed in 2010 by a Congress then controlled by Democrats and signed into law by Obama.
Fifty-four percent of those questioned say they oppose the law, also relatively unchanged since 2010.
The survey indicates that 35 percent oppose the health care law because it's too liberal, with 16 percent saying they oppose the measure because it isn't liberal enough.
The wide partisan divide over the law remains. Nearly three quarters of Democrats say they favour the Affordable Care Act. That number drops to 16 percent among Republicans.
"Not surprisingly, the Obama coalition is most supportive of Obamacare," says CNN Polling Director Keating Holland.
"A majority of younger Americans favour the new health care law; support among other age groups falls as low as 31 percent among senior citizens.
"Only a third of whites support the law, compared to six in 10 non-whites. Obamacare also wins majority support in urban areas and in the Northeast, the bluest region of the country," he notes.
The CNN poll, conducted May 17 and 18, right after the Republican-controlled House voted to symbolically repeal the entire law for the third time in three years, surveyed 923 adults. It has a three-point margin of error.