Treaties have the standing of laws, and cannot alter the Constitution any more than ANY law can.
Correct, treaties cannot override the Constitution. However, as applied to the UN Small Arms Trade Treaty (or the CIFTA Treaty), that leaves us with two big problems.
Problem #1 is that at least 3 of the existing Supreme Court Justices (and likely 4 if we include Kagan) do not believe that an individual right to bear arms even exists in the Constitution. So they would have no problem finding this treaty constitutional if it were challenged in the Supreme Court. That leaves us either one or two votes away from losing if one of the majority from Heller is replaced by someone with a different view.
Problem #2 is that in the past week, several of the nations made calls for centralized registration of all firearms as a part of the treaty. So far, no case has challenged the constitutionality of registration of firearms and in fact, the argument that it is constitutional is good enough that even with no change in the current SCOTUS line-up, we might still lose that vote.
Right now, our biggest advantage is that the Senate hasn't shown the slightest inclination to ratify this treaty or any other arms treaty. For that reason alone, I don't consider the Arms Trade Treaty a very serious threat; but I don't think we should be complacent about it either. The reason it isn't a threat is because Senators on both sides understand that would cost them their jobs. We want to continue to make sure they don't forget that point.