Militia (noun)
o a military force that is raised from the civil population to supplement a regular army in an emergency.
o a military force that engages in rebel or terrorist activities in opposition to a regular army.
o all able-bodied civilians eligible by law for military service.
The National Guard is an oddly a grey entity. While they fit the description of a militia, they simultaneously recognized by the US as state-funded reserve forces - they even have their own federal pay code for training/duty with the Army. They are rarely called upon for anything other than CONUS emergencies; whereas the US military focuses mainly on OCONUS. But, as I alluded to, they answer to their state AND the federal government... so taking government munitions and giving them to another entity subordinate to the government is likely not going to accomplish what you'd like to accomplish.
But whether or not we should give nuclear armaments to Joe Civilian, a particular state or a militia is a silly debate. As I said before, while the 2nd amendment doesn't explicitly ban it, there are laws already on the books that do. Whether that is in keeping with the Constitution is a question for SCOTUS.