In a shocking one-month swing, Mitt Romney stormed into the lead over President Barack Obama in a new Pew Research poll conducted after Romney's consensus victory in the first presidential debate.

The poll finds a 12-point swing among likely voters. In Pew's last poll, conducted in the middle of September, Obama led Romney 51-43 among likely voters. Now, Romney leads 49-45.

The shift is due to Romney shoring up key areas of strength among likely voters and improving his overall image, much of which can be attributed to his strong debate performance. Sixty-six percent of voters thought Romney won the debate, compared with just 20 percent who said Obama won. Among Independents, Romney won by an astounding 78-14 margin.

Romney's overall favorability rating climbed 5 points from September and hit 50 percent for the first time ever in Pew's survey. Notably, he bests Obama, whose favorability rating has dropped from 55 percent to 49 percent.

He also has boosted his standing with voters on the economy and jobs. He now leads Obama by 8 points on which candidate would best "improve the job situation." Last month, Obama led Romney by a point in that category.

Romney also saw significant gains among women. Last month, women preferred Obama by an astounding 18 points. Now, they are equally split between both candidates at 47 percent apiece.

The poll sampled 36 percent Republicans, 31 percent Democrats and 30 percent Independents. It's notable because most polls over the past two years have found higher samples of Democrats, leading to recent charges of bias and so-called "unskewing" of results.

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