The USC Annenberg/Los Angeles Times poll shows the president leading 48 percent to 45 percent among all voters and 48 percent to 46 percent among likely voters.
While likely voters are evenly divided on Obama's job performance, they tend to like him better than Romney. More than half, 53 percent, have a favorable view of the president and 45 percent an unfavorable one, while their views of Romney tilt the other way 46 percent to 48 percent.
The barrage of negative ads coming from both sides has done little to move those numbers, pollsters say.
The poll was conducted by a Democratic firm, Greenberg Quinlan Rosner Research, and a Republican one, American Viewpoint.
"The description for this race is 'static,'" said Drew Lieberman, a Greenberg Quinlan pollster.
The poll found support for Obama's plan to increase taxes on high-income households. While 43 percent supported Obama, 37 percent disagreed. Independents, however, supported Romney's position 42 percent to 38 percent.
On another hot-button issue, giving a path to citizenship for some young illegal immigrants, likely voters supported Obama's proposal 2-1.
The polling firms surveyed 1,009 registered voters Aug. 13-19, with 954 in the sample considered likely voters. The margin of error was 3.1 percentage points for the entire sample and 3.2 points for likely voters.