Umm, no the National Guard isn't a civilian military. The National Guard fills any number of roles.
On one level, it is an organization for state militias. In this regard, it is a "state military" that can work with state agencies and domestic federal agencies.
It is also a reservist force for the military. The National Guard can be called for overseas service working with the branches of the U.S. military.
The National Guard can also be federalized and used for domestic purposes on behalf of the federal government under very specific circumstances, which mostly covers riots or civil disturbances. Otherwise, the federal government has no military powers on domestic soil - this is the Posse Commitatus Act, and it was passed by Southern Senators after Reconstruction to limit federal power in the South.
This is why Obama, and others, are calling for a "civilian force" as large as the military - because the federal government has very few powers to deal with domestic issues.
One example of this was during Hurricane Katrina. President Bush tried to assert his authority to secure New Orleans during the aftermath, but was prohibited from doing so because of Posse Commitatus. He even went so far as to try to get a U.S. Army officer sworn into the Louisiana National Guard, but that didn't go through.
So, more likely than not, such a civilian force would be most likely geared towards riot control and federal response to manmade and natural disasters. Personally, I wouldn't mind if the National Guard was federalized more but made a purely domestic force and unable by law to be deployed overseas for these reasons. I also think the National Guard along with the Coast Guard be attached to the Department of Homeland Security instead of the Department of Defense as it is now.
So while there are fears of some kind of personal army, such a force would mostly be used for federal disaster response. I don't know how the specifics of it should work, because it will all be quite political, but I do think that the federal government should have a better ability to respond to domestic crises and disasters, and I think that's how it should be geared towards.