I've heard all about this sort of thing when I bought my first gun (ten years ago now). The idea that the President would try to use an international treaty to ban firearms is nothing new.
Treaties have to be ratified by the Senate, as some folks above pointed out. I am not an expert on international law, but as far as I understand it, ratified treaties can only affect the enforcement of local and federal laws. Again, not saying I'm an expert, but as far as I know, a treaty cannot nullify an individual's rights protected by the Constitution. Example, the UN cannot take away your right to freedom of worship, freedom of speech, right against unreasonable searches, right against self incrimination, etc. by way of a treaty.
I'm not afraid of the guy who wants many guns; I'm afraid of the guy who wants just one.