General Discussion

Sounds like the only one to stand in his way is potentially Secretary of Defense (Kegsbreath). There may have been some issue, but by saying 'he wanted the codes" makes the whole story sound fishy (unknowledgeable). There are no codes he needs to be given by anyone.

Quick search says:

The President has the authorization codes, known as "the biscuit," on their person at all times, rather than asking for them. As the sole authority for nuclear use, the President can order a strike without advisor consultation, but they do not physically press a button; they identify themselves via the codes to the Pentagon.

Key Aspects of the Nuclear Command System:
The Biscuit & Football: The president carries a plastic card the "biscuit", with codes to identify themselves, which are used in conjunction with the "nuclear football," a briefcase carried by a military aide containing launch options.

Sole Authority: The President holds the exclusive power to authorize a nuclear strike. There is no legal requirement to consult with the Vice President, Congress, or military advisors, though the Secretary of Defense must confirm the order.
The Chain of Command: While the President authorizes the strike, the order is transmitted through the military chain of command, where officials must ensure the order is lawful, though they cannot legally prevent an authorized strike.
No "Button": The system is designed to verify the identity of the Commander-in-Chief rather than operate via a simple button press.

While some users on Reddit and Quora speculate that the president only holds part of the code or requires a second code from the Secretary of Defense, official information highlights the president's sole authority and possession of the authentication "biscuit".