The Democrats said they are "puzzled" by McDonnell's Oct. 9 letter to President Obama, in which he said he supports House Republican legislation that would shift planned spending cuts away from defense and toward many social programs.

"On behalf of all Virginians, I ask you to help prevent the potential degradation of our defense and the negative impact on our economy that will surely result if sequestration is allowed to take effect this January," McDonnell wrote. He was referring to the Sequester Replacement Reconciliation Act, H.R. 5652, which the House approved in May.

But the Democratic letter said shifting the cuts to defense would not spare Virginia, and would particularly hurt Virginia residents who are relying on various federal programs.

"By directing all spending reductions to the non-defense discretionary account, H.R. 5652 is certain to trigger an even greater loss to Virginia … delivering a devastating blow to Virginia's economy and its at-risk residents," they wrote.

"As you know, Virginia is home to one of the largest concentrations of federal workers in the nation, so that would be particularly harmful to our residents and economy."

The letter ended by asking McDonnell to encourage House Republicans to support a bipartisan plan for avoiding tough sequester cuts that includes new tax revenues, something they say McDonnell has supported in the past.

"So we hope you will join us in calling on Speaker BoehnerJohn Andrew BoehnerGOP revolts multiply against retiring Ryan Can Jim Jordan become top House Republican? Tensions on immigration erupt in the House GOP MORE and Majority Leader Cantor to begin discussions on a balanced deficit-reduction package that can garner bipartisan support," they wrote.