The Morning Consult poll conducted after the debates found that 32 percent of potential Democratic primary voters selected Biden as their top-choice candidates, compared to 33 percent after the first Democratic debate in June.
The first Democratic debate did result in more changes, with Harris spiking from 6 percent support to 12 percent while Biden slid down from 38 percent.
In the latest poll, conducted Aug. 1, researchers surveyed 2,419 registered voters who said they might vote in a Democratic primary or caucus. The results have a margin of error of plus or minus 2 percentage points.
Biden, Harris, Warren and Sanders are among just 7 of more than two dozen contenders who have already qualified for the September debates. Biden has consistently polled as the front-runner.