The Fifth Amendment to the United States Constitution states, in part, "No person shall be ... deprived of life, liberty, or property, without due process of law." Since the 1930's, the Supreme Court has paid particular attention to the word "due"; the Fifth Amendment is saying that a liberty cannot be infringed unless a process of law which is "due" or appropriate is undertaken. But then the question arises, what if some liberties are so fundamental that no process of law can ever be fitting to take those liberties away? So the Supreme Court has developed a doctrine called "substantive due process", according to which the Fifth Amendment is not just a procedural guarantee about what processes of law the government applies when depriving you of liberties, but also a substantive guarantee about the government not taking away certain fundamental liberties regardless of what processes of law they use.
I was reminded of this in the context of the bills being debated in Congress right now, about stopping people on the Terrorist Watch List from buying guns. A common objection to such legislation is that this would deprive Americans of Second Amendment rights without due process, since the government can put someone on the list even if they haven't demonstrated evidence to a judge. (Although there are also modified versions of the bill that would provide such due process.)
My question is, is the Second Amendment right to bear arms one of the fundamental liberties covered by the substantive due process doctrine? Are there any court cases that address this?
I'm guessing that the Second Amendment isn't covered by substantive due process; otherwise I think the federal background check laws we have now would probably have been ruled unconstitutional.