Okay, time to talk about the supremacy clause
"and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby"
Generally, that's the part that gets repeated, supreme law of land is stressed, and people get undies in a bunch.
However, the full text is a bit more enlightening
"This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby, any Thing in the Constitution or Laws of any State to the contrary notwithstanding."
Note that there are actually 3 items listed that constitute the supreme law of the land.
2. Laws made after the Constitution, but following it's rules (51% in senate +51% in house + pres signature, or 67% senate + 67% house override of veto)
Obviously, category #2 can be overturned by the Supreme Court due to conflicts with the Constitution, so 'supreme' doesn't mean a whole lot. Treaties, too, in as far as they overstep the Constitution can be struck down as well.
So why the term 'Supreme Law of the Land'?
because our legal system at it's heart is a 'Common Law' system, which means the decisions of previous judgments are what are used to decide cases. The idea being is everyone gets treated fairly then. ( If act A is a crime when person X commits it, then it is a crime when person Y commits it too. If X and Y are of different social standings, without common law it would be okay for Y to get away with it)
Hence a judge's decision sets 'legal precedent' and that actually legally binds judges who serve at a similar level.
So what happens when a judge makes a decision and sets a legal precedent that people dislike? Well, they create a new law. Due to the Supremacy Clause, this law supercedes the previous decisions made.
What also throws some people is the end phrase of
"any Thing in the Constitution or Laws of any State to the contrary notwithstanding"
Note it says 'the Constitution' not 'THIS Constitution' The Constitution of the United States of America is recognizing that there are and will be OTHER constitutions, no matter how much we seem to forget it and term the C of the US of A as simply 'The Constitution'
It is best read as 'any thing in the Constitution of a State or Laws of a State'
As Notwithstanding means 'despite' it fully means
Constitution, Federal Law, Federal Treaties bind EVERYONE of this land Despite anything in State Law or State Constitution that say different'
Hence, Obama can sign a treaty but it won't LEGALLY affect our RKBA.
Of course, many current ILLEGAL laws are on the books and enforced. We are best served by NOT getting such a treaty approved.