Fifty-two percent of respondents said they favor repealing or scaling back the law, up from 50 percent in mid-October, Gallup reported.
Of the latest total in the latest poll, 32 percent said they would repeal the law and 20 percent favored scaling it back.
At least 50 percent of Americans have said they would repeal or change the law since Gallup began asking the question in January 2011.
Twenty percent said they want Congress to expand the law, up from 14 percent in October.
Seventeen percent said they want the law to be kept as is, down from 24 percent, Gallup said.
Sixty-eight percent of Republicans said they want the law repealed -- an increase from 57 percent in October.
Thirty-four percent of Democrats said they want Congress to expand the law, up from 22 percent in October.
The most recent survey was conducted after a series of technical issues plagued the website, which opened Oct. 1, preventing many Americans from successfully signing up for coverage.
The survey was conducted by telephone Dec. 3-4. The margin of error was 4 percentage points.