Even with regard to active duty military, I think they can do everything except actual law enforcement. And could probably even do force protection while they were involved in other activities - whether they be logistical, SAR, or whatever.
The problem with martial law - and there are problems with it - is that this then becomes a Federal problem, all the way around. I don't think they could workably delegate LE to the US military while retaining other functions on a state or local level. I don't think LA or NO want that, and I don't think Washington wants that.
Thanks for responding. I was thinking that the president was probably trying to encourage the Governor to declare martial law so he could send in the Army and Marines to help with law enforcement vs just search and rescue sort of stuff. But if there are problems with martial law and you think none of them want it, then I'll have to re-evaulate.