Kaine spoke at the Democratic Party of Virginia's annual Jefferson-Jackson dinner in Richmond. He said whether he runs or not, he is confident the next senator from Virginia will be a Democrat.
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Meanwhile, former Democratic National Committee chairman Terry McAuliffe is all but writing off a run for the U.S. Senate in 2012.
Webb announced earlier this month that he will not seek re-election, leaving Democrats scrambling to field a strong candidate to keep the seat.