Treaties are signed every ten years between the United States and Russia reducing nuclear weapons by a third. These two countries have the most nukes in the world, so if they are reducing nuclear weapons then there is wide support for them. The rest of the world isn't ready to give nuclear weapons to other countries such as North Korea and Iran.
Nuclear weapons is a part of worldwide stability. All of the large countries can rely on nuclear weapons to help keep peace and as well as deter. It will help the strongest nations have a reason to keep peace amongst each other as well as help prevent a series of conflicts.
If the United States of America were to abolish nuclear weapons, Russia and China would most likely not "play fair" and agree to do the same. We would be virtually defenseless against two of the most powerful nations in the world. It is a terrible idea to abolish nuclear weapons.