Final answer:
President Johnson's use of a Bible verse is an example of an allusion; it's an indirect reference to something without explicit mention, connecting current issues to a broader historical and spiritual context.
Step-by-step explanation:
President Johnson's reference to a Bible verse, Matthew 16:26 King James Version, represents an instance of an allusion. An allusion is an expression designed to call something to mind without mentioning it explicitly. It serves as an indirect or implied reference. Here, Johnson is not creating an extended symbolic narrative that would qualify as an allegory, nor is he using exaggerated language which would be considered a hyperbole, and since he is not comparing two unlike things, it is not a metaphor.
Utilizing an allusion in his speech, President Johnson connects the current challenges the audience is facing to the broader historical and spiritual contexts by referencing sacred texts, which may invoke an ethos-based appeal linking to the patriotic and religious sentiments of his listeners.