This is essentially false. There are several redundant safety and security mechanisms protecting nuclear weapons, one of which is the Permissive Action Link (essentially a combination lock on the warhead). This is the component in question which once had the alleged code of 00000000: https://web.archive.org/web/20120511191600/http://www.cdi.or...

The "nuclear football" is a completely separate authentication mechanism for verifying a presidential order, and as far as we know uses codes that rotate on a daily basis.