It seems the National Guard is the Constitutional militia, subject to dual missions to both state and federal jurisdiction.
The Governor can call out the guard on federal money, but there seems to have been some dispute over federal funding in the past.
Posse Comitatus applies for federal missions, Posse Comitatus does not apply for state missions.
Militia Act of 1792: http://www.constitution.org/mil/mil_act_1792.htm
It is my belief that state mobilization of the National Guard has been generally unarmed since Kent State. http://history1900s.about.com/od/1970s/qt/kentstate.htm
Katrina: Governor Orders Troops to Shoot and Kill Looters
Despair is also affecting those in New Orleans charged with protecting the city, said State Police Superintendent Col. H.L. Whitehorn. Some New Orleans police officers have resigned rather than face the violence in the city. “It’s my understanding those who have resigned said they have lost everything and it’s not worth being shot at and losing their lives,” Whitehorn said. Whitehorn said he did not know the specific number of police officers who have quit their jobs.
Under riot conditions, shooting armed perpetrators in the midst of violence may be a necessary evil. Shooting unarmed television thieves, though, is hard to justify. And, of course, without benefit of a trial we may wind up shooting people “stealing” their own possessions.
While on patrol in a mostly vacant part of New Orleans about 1 a.m. on March 9, National Guard troops spotted Terry Burton riding a bicycle and carrying a hacksaw. A National Guard spokesman later told reporters that the guardsmen followed the 53-year-old Burton, who National Public Radio described as "mentally ill", because there had been many thefts of copper pipe in the area. When the soldiers approached Burton he reportedly threatened them with a knife, and then threw broken glass at them, injuring a sergeant.
The guardsmen then followed Burton into an empty house, where he pointed what appeared to be a rifle at them. After one soldier shot Burton several times, killing him at the scene, they learned that he was only holding a BB gun.
The guardsman was removed from patrol duty, the spokesman said.
Not taking any sides -
Legal discussion concerning right to bear arms, some legal confusion as to what second amendment really means concerning armed state government militia under ultimate federal control vs individual right to posses: