The McClatchy-Marist poll showed the former Alaska governor and vice presidential nominee trailing the president by just 5 points -- with Obama leading 49-44 percent.
The poll showed Palin, who has not announced a bid for president, doing better than several candidates who have. The poll showed Texas Gov. Rick Perry trailing Obama by 9 points and Minnesota Rep. Michele Bachmann trailing by 13 points. Former Massachusetts Gov. Mitt Romney was behind by 2 points.
The new poll also showed Palin leading among independents in the general election, and moving into the top tier behind Perry in the GOP nomination contest.
But it also showed a large majority of voters do not want her to enter the race.
According to the survey, 72 percent of Republicans and GOP-leaning independents don't want her to run in 2012.
The poll also showed former New York City Mayor Rudy Giuliani leading the president in a general election, but showed most Republicans don't want him to run either in 2012.
The survey of 1,042 adults had a margin of error of 3 percent.