Pablo Martinez Monsivais / AP President Barack Obama speaks at a campaign event at Rollins College in Orlando, Fla, Aug. 2, 2012.

President Barack Obama has opened a narrow lead in Florida as Republicans gather in Tampa this week to nominate Mitt Romney, according to a new TIME/CNN/ORC poll. The survey also found the two candidates locked in a near tie in North Carolina ahead of the Democratic convention there next week.

Obama holds a 50%-46% over Romney among likely voters in Florida. In North Carolina, the two candidates are locked in a virtual dead heat, with Romney up 48%-47%. In both states, the poll, conducted from Aug. 22 to Aug. 26, has a margin of error of 3 percentage points.

Obama’s edge in Florida is bolstered by women voters, among whom he’s beating Romney 54%-42%, and by nonwhite voters, with whom he boasts a 70%-29% advantage. There are signs the incumbent is stitching together the same demographic coalitions that helped him capture Florida’s 29 electoral votes four years ago. Obama holds an eight-point lead among urban voters and a 13-point margin (54%-41%) with voters under 50. He also racks up 58% of self-identified “moderates” and manages to siphon off nearly one quarter of self-identified conservatives. In the sprawling, diverse Sunshine State, the President performs best in the Miami region, where he garners the support of 63% of respondents.

Romney holds a sizable advantage among white voters in Florida, 56%-38%, and in particular white men, with whom he leads 58%-37%. Despite Romney’s decision to select Paul Ryan, the architect of a plan to refashion Medicare into a voucher system, as his running mate, the GOP candidate holds a two-point lead among voters over 50, including a 51%-45% edge with those over 65. Romney has also piled up a 25-point cushion in northern Florida, the state’s most conservative region, and a 53%-45% edge among respondents earning more than $50,000 per year. The two candidates are virtually deadlocked among self-identified independent voters in this fall’s biggest battleground. In a state where Republican officials have been aggressively seeking out ineligible voters to purge from the rolls, Obama’s overall lead among registered voters swells to nine points.

Obama’s demographic advantage among nonwhite voters is keeping him competitive in North Carolina, a conservative state where he pulled off an upset four years ago. The President has the support of 84% of such voters in the TIME/CNN survey, along with 60% of respondents who reside in urban areas and 56% of those making under $50,000. Obama also garners 59% of the Tar Heel State’s self-described moderates. His strongest geographic regions are the eastern swath of the state and the affluent Raleigh region, a high-tech hub dotted with universities.

But a week before Democrats arrive at their national convention in Charlotte, there are signs that Obama faces an uphill battle to keep the state in his column. Romney boasts a 53%-40% lead among self-described independent voters. His 30-point lead among white voters includes a 12-point edge among white women, and he has amassed leads of 15% and 12%, respectively, among suburban and rural voters. Among respondents earning more than $50,000 per year, the Republican challenger has a 7-point lead, and he has opened a 15-point cushion among voters 50 and older.

In Florida, a total of 1,020 respondents, including 895 registered voters and 776 likely voters, were interviewed by telephone by ORC International from Aug. 22 to Aug. 26. In North Carolina, 1,019 respondents were surveyed on the same days, including 905 registered voters and 766 likely voters. The poll’s margin of error for both states is +/- 3 percentage points.