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Mitt Romney's debate performance pushed him into a national lead over President Obama among likely voters, Pew Research Center reports in its latest poll numbers. Romney is leading Obama 49 percent to 45 percent in a poll taken over four days after the debate last week, even though in mid-September, Obama was leading Romney by 8 percentage points. There's a ton of good news for Romney in this poll:

Two-thirds of registered voters think Romney won the debate, while only a fifth think Obama did.

Romney's favorable rating hit 50 percent among registered voters for the first time.

Voters think Romney is the candidate of ideas by 47 percent to 40 percent.

Romney and Obama are tied as to who would be a strong leader—even though Obama had a 13-point lead on that question last month.

Romney has an 8-point lead on jobs.

Voters still think Obama is the candidate who's more moderate, honest, and consistent.

Other pollsters have found Romney crushed Obama in the debate, too -- Gallup says Romney was seen as the victor by the biggest margin in its history. But Gallup hasn't yet measured such a big swing toward Romney in national polls, showing Obama ahead 50 percent to Romney's 45 percent.

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