George Allen and Tim Kaine have a Washington problem. Allen, a Republican, and Kaine, a Democrat, were both popular governors in Virginia. But each also has close ties to Washington, Allen as a senator from 2001 to 2007 and Kaine as President Obama’s handpicked chairman of the Democratic National Committee from 2009 until this year.

Now, with both men running to become their party’s 2012 U.S. Senate nominee, those ties are complicating both of their efforts to portray themselves as the kind of independent political outsider that would appeal to the state’s swing voters.