The CNN poll showed 58 percent of voters felt Romney had shown himself as a stronger leader, with 37 percent saying Obama. The two even tied on likability, an area in which Obama usually has a wide lead. Romney led by 12 points on the question of who would best handle the economy, a big swing from a pre-debate poll by the network showing the two tied on the issue.

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CNN's poll sample skewed Republican compared to most registered voter polls, which likely inflated Romney's numbers.

The polls also suggest the potential for a major impact on the race: 35 percent of voters in the CNN poll said the debate made them more likely to vote for Romney, while just 18 percent said Obama.

The president has been leading in national polls for months, though by a narrow margin.

