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Rick Perry’s campaign sees carrying the South in the nomination race as critical and the data from the capital of the Confederacy gives him reason to be optimistic,” Mr. Brown said.

Mr. Perry had 51 percent of the vote among white, evangelical Christians, compared to 29 percent for Mr. Romney.

In the closely watched race for the seat of retiring Democratic Sen. Jim Webb, Republican George Allen and Democrat Tim Kaine, both former Virginia governors, are in a dead heat.

Mr. Allen holds a 45 percent to 44 percent lead over Mr. Kaine, statistically unchanged from June when Mr. Kaine led 43 percent to 42 percent. However, Mr. Kaine hold a 42 percent to 40 percent advantage over Mr. Allen among independent voters in a head-to-head race, according to the poll.