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Romney tops Obama among likely voters 47 to 44 percent, down from his 51 to 43 lead in the same poll from May.

While a negative favorability rating dogged Romney throughout the GOP primaries, his favorability rating in North Carolina is positive, according to Rasmussen, with 50 percent saying they have a positive view of the former Massachusetts governor versus 46 that hold a negative image.

North Carolina is one of 12 key swing states the president won in 2008 that the GOP is looking to reclaim. Democrats will hold their national convention there in September.

Obama defeated Sen. John McCainJohn Sidney McCainLessons of the Kamala Harris campaign Overnight Defense: Trump clashes with Macron at NATO summit | House impeachment report says Trump abused power | Top Dem scolds military leaders on Trump intervention in war crimes cases Top Armed Services Democrat scolds military leaders on Trump's intervention in war crimes cases MORE (R-Ariz.) in the Tar Heel state by less than 1 percent in 2008, the first time North Carolina had voted for the Democratic presidential candidate since 1976.

The Rasmussen survey of 500 likely voters was conducted on June 25 and has a 4.5 percentage point margin of error.