The JCS had to have the codes: look at the 1998 exchange, for starters. And given how things were going, using nukes to shatter Mexican supply lines and use a low-yield TLAM-N or ALCM on the Presidential Palace in Mexico City (10 KT) would have been very appealing, given the lack of conventional forces available to deal with the invasion. There are proceedures in place that, if the communication links to civilian leadership fail, the military takes over until a Presidential successor can be found. And that includes having nuclear release authority.
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Treat everyone you meet with kindness and respect, but always have a plan to kill them.
Old USMC Adage
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