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U.S. Rep. Bobby Scott is the only other Democrat said to be seriously considering running for the Democratic nomination.

Along with Mr. Allen, tea party favorite Jamie Radtke and Hampton Roads lawyer David McCormick also have declared their bids for the GOP nomination.

Other prospective Republican candidates include conservative firebrand Delegate Robert G. Marshall of Prince William County as well as Corey A. Stewart, chairman of the Prince William County Board of County Supervisors. Tim Donner, founder of Horizon Television in Great Falls, also is weighing a bid.

If the race comes down to a likely matchup between Mr. Kaine and Mr. Allen, Mr. Goldman gives Mr. Kaine a slight edge for his access to Mr. Obama’s fundraising abilities and his holding public office more recently. Mr. Kaine served as Virginia governor from 2005 to 2009, while Mr. Allen’s last political victory was in 2000.

But that advantage is very slight, Mr. Goldman said.

“There’s no evidence right now that Kaine can put his name on the ballot and just go to sleep,” Mr. Goldman said.

Stephen Dinan contributed to this story.