What a ridiculous statement! A process like you describe would take months or years, while thousands of people might die from starvation, dehydration, violence, disease, and lack of medical care due to the incompetence of state and local authorities in the next few weeks. Besides, there is precedence for Federal intervention in these matters.
The Posse Comitatus Act, passed after Reconstruction, placed curbs on involvement in law enforcement on the part of the U.S. Army, and by extension the Air Force, which evolved out of the Army. It does not address the Marines or the Navy, which was and is under the authority of the Navy Department, not the War (Army) Department. Nor does it address the Coast Guard, which is an agency of the Treasury Department, but which is transferred to the Defense Department in wartime.
Moreover, the Executive Branch of government is charged with the duty of protecting Federal civilian workers, such as FEMA employees. The local and state authorities are not doing their job in this respect. The Federal marshals in Little Rock in 1957 were not protected by the local authorities, prompting Eisenhower to send in the regulars and place the National Guard under Federal authority.
There is an old saying to the effect that the Constitution is not a suicide pact. Thousands of lives are in peril in New Orleans due to the incompetence of state and local governments. This is more severe a situation than the integration crisis of the 1960s or the Terri Schiavo court-ordered dehydration earlier this year because of the human cost. Let's not excuse Federal inaction under the rubric of states rights or the rule of law.
I see you aren't willing to press Congress to change the Constitution or the laws that forbid the use of the military in this situation.
I won't vote for your option that the president disobey the law.