This is an interesting question, and one that a few brief minutes searching the usual sources doesn't turn up an obvious answer (or even much discussion). Moving the capital doesn't appear to have been seriously considered at the time.
It is easy to find lots of information on Washington DC's civil war defenses - some ~70 forts, 400 emplacements for field guns, and unmatched transportation/communication infrastructure. The resources devoted to protecting the capital instead of campaigning were a regular source of contention for Lincoln, his generals, and public opinion - many opportunities were missed by Army of the Potomac commanders who feared leaving DC vulnerable.
On the other side, the Confederate capital was originally in Montgomery, Alabama, and moved to Richmond, Virginia when Virginia seceded following Fort Sumter. Like Washington, this put the capital remarkably close to the front lines, but the existing industry, infrastructure, political weight, and defensibility seemed to make the position worth the risk.
The world was bigger and slower back then. If southern troops were mobilized, there would be days or weeks of warning before they got to DC. By that time, the politicians could retreat, and replace themselves with union soldiers.
It is easy to find lots of information on Washington DC's civil war defenses - some ~70 forts, 400 emplacements for field guns, and unmatched transportation/communication infrastructure. The resources devoted to protecting the capital instead of campaigning were a regular source of contention for Lincoln, his generals, and public opinion - many opportunities were missed by Army of the Potomac commanders who feared leaving DC vulnerable.
On the other side, the Confederate capital was originally in Montgomery, Alabama, and moved to Richmond, Virginia when Virginia seceded following Fort Sumter. Like Washington, this put the capital remarkably close to the front lines, but the existing industry, infrastructure, political weight, and defensibility seemed to make the position worth the risk.
Hoping someone with knowledge chimes in :).