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A poll released Wednesday by Quinnipiac University also found the race close, with Kaine leading 48-46 percent.

"Virginia's U.S. Senate has been a dead heat since it began," Peter A. Brown, assistant director of the Quinnipiac University Polling Institute, in a statement. "It's pretty clear that whether George Allen or Tim KaineTimothy Michael KaineDemocrats turn on Al Franken Avalanche of Democratic senators say Franken should resign Senate panel moves forward with bill to roll back Dodd-Frank MORE becomes the Old Dominion's next senator, it almost certainly will be by a razor-thin margin."

The same Rasmussen poll found President Obama with a 48-46 percent advantage in Virginia over presumptive Republican nominee Mitt Romney. The poll carried a margin of error of 4.5 percent.