One, there's a much stronger argument to be made that artillary are seperate from the notion of arms than with something like an "assault weapon".
Two, there's multiple international treaties we're involved in that have legal regulations regarding the obtaining of nuclear material and weapons and treaties are given constitutional weight and thus could cut into the notion of the 2nd amendment even if nukes were covered under it (by the way, this is partially why people are very adverse to signing UN treaties regarding firearms)
Third, it's an inherently massively unrealistic situation. There's a reason why various terrorist groups or despot leaders of countries are routinely trying to garner a nuclear bomb but aren't able to...because it's far from taking a stroll down to the local walmart and picking one up in terms of difficulty. The likelihood of a citizen that poses any kind of threat actually obtaining a nuclear weapon, even if legal, would be ridiculously small.
But nice job gun-godwining