A Floridian gets assistance with the health care exchange site on Oct. 3.
Washington (CNN) - Support for the country's new health care law appears to be rebounding slightly, according to a new national poll.
A CNN/ORC International survey released Tuesday indicates that nearly all of the increased support comes from upper-income and college-educated Americans.
The poll's Tuesday release comes on the same day that a special election is being held in Florida's 13th Congressional District to fill a vacant U.S. House seat. Obamacare has become a major issue in the competitive contest to fill the remainder of the term of the late GOP Rep. Bill Young.
According to the poll, 39% of Americans say they support the health care law, up from 35% in December, a record low in CNN polling. The uptick of four percentage points is within the survey's sampling error. Fifty-seven percent of those questioned say they oppose the measure, down five points from December.
"Not all of the opposition to the health care law comes from the right," said CNN Polling Director Keating Holland. "Thirty-nine percent say they oppose the law because it's too liberal, but 12% say they oppose it because it's not liberal enough."
That means half the public either favors Obamacare, or opposes it doesn't go far enough. Roughly 6% oppose the law but don't have an opinion on whether it is too liberal or not liberal enough.
The poll indicates that the rebound in support for Obamacare has come almost entirely among upscale Americans. The law made no headway among people who make less than $50,000 - 35% of them supported it in December, and 35% support it now. But among people who make $50,000 or more, support rose from 36% to 46%.
"The same pattern holds true for college education - virtually no change among people who never went to college, but a nine-point change among those who did," Holland adds.
The CNN poll was conducted by ORC International from Friday through Sunday, with 801 adults nationwide questioned by telephone. The survey's overall sampling error is plus or minus 3.5 percentage points.
CNN Political Editor Paul Steinhauser contributed to this report.
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