The UN was told that the US would not participate in the ban of firearms:

A remarkable thing happened at the United Nations yesterday. We, the United States, told the world “no”. The messenger was Robert Joseph, the Undersecretary of State for Arms Control and International Security. Speaking before the dozens of nations that have gathered for the review conference on Small Arms and Light Weapons, Joseph told the world in no uncertain terms where the United States stood.

“The U.S. Constitution guarantees the rights of our citizens to keep and bear arms, and there will be no infringement of those rights,” he proclaimed to the dignitaries and functionaries. “The United States will not agree to any provisions restricting civilian possession, use or legal trade of firearms inconsistent with our laws and practices.”

What did the UN want to do?

The illicit trade in small arms and light weapons can be exacerbated by the unregulated possession of small arms and light weapons by civilians not part of responsible military and police forces. The measures below can contribute to addressing this aspect of the illicit trade in these weapons.
(a) States will establish appropriate national legislation, administrative regulations and licensing requirements that define conditions under which small arms and light weapons can be acquired, used and traded by private persons.
(b) States will seriously consider the prohibition of unrestricted trade and private ownership of small arms and light weapons specifically designed for military purposes (e.g., assault rifles, machine guns, grenades and high explosives produced for military purposes).

Any agreement with this type of provision would clearly be unconstitutional.
Read the rest here.