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 McCainThe peculiar priorities of Adam Schiff Ocasio-Cortez fires back at Lindsey Graham: 'Graham wants to bring back 1950s McCarthyism' Meghan McCain knocks Lindsey Graham for defending Trump's tweets: 'This is not the person I used to know' 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.