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Mr. Goldman said he knows of at least one Virginia race in recent history that was impacted by a presidential contest: the 1972 Senate race, in which Republican William L. Scott road the coattails of Richard Nixon’s successful re-election campaign to defeat Democratic candidate William B. Spong.

Mr. Nixon carried Virginia and 48 other states — all but Massachusetts — in his victory over Democratic Sen. George McGovern that year.

Still, Mr. Holsworth thinks a more accurate measure of where the 2012 Senate race in Virginia stands is the president’s polling against Republican candidates, rather than his job-approval numbers.

“A 40 percent approval rating doesn’t mean you’re going to get 40 percent of the vote,” he said. “In politics, you always have to run against somebody.”

Indeed, Mr. Obama’s numbers against would-be contenders have more closely tracked with his approval ratings. A poll released shortly after his self-professed “shellacking” in the 2010 midterms, showed him with a 48 percent-43 percent lead over former Massachusetts Gov. Mitt Romney and a 49 percent-44 percent lead over former Arkansas Gov. Mike Huckabee, who at the time was still weighing a bid. Only in the most recent Quinnipiac poll have would-be GOP challengers truly caught up, with Texas Gov. Rick Perry and Mr. Romney within the margin of error of the president.

Though Mr. Kaine and Mr. Allen are certainly well-known, a big question is to what extent will their race be fought on Virginia or national issues.

“I think that’s an open question right now,” Mr. Holsworth said. “For a vast majority of voters, it’s going to be viewed through the national lens. If you look at what happened in the congressional races in 2010, they were entirely nationalized.”

For example, Democratic then-Rep. Rick Boucher, elected in 1982 to represent Virginia’s Southwestern 9th Congressional District, was toppled by then-Virginia delegate and GOP challenger H. Morgan Griffith in 2010. Mr. Bouchers support of the “cap-and-trade” climate bill regulating carbon emissions played a huge role in the campaign and his surprising loss, though it was Mr. Boucher who helped shape the bill and make changes that he said protected the region’s coal industry.

Another issue is to what extent Mr. Kaine will attempt to distance himself from the president when he campaigns in Virginia, an important swing state he won in 2008 to become the first Democratic presidential candidate in more than four decades to take the state.

“There will be a few places where [Mr. Kaine] will certainly talk about Virginia’s interests, rather than national interests,” Mr. Holsworth said. “But overall, there’s only so much of that he can do — politically and personally. And Obama can’t give up on Virginia. He needs to be here a lot. I don’t think Kaine can win Virginia if Obama’s not competitive here. I just don’t see it.”