I don't know which “military leaders” you have in mind, but the Joint Chiefs of Staff were well-aware of Reagan's internal NSC directives in the first two years of his administration to take on the Soviets through economic warfare, covert operations, and increased defense spending.
Read the Book Reagan’s Secret War by Martin Anderson
Tells how he had to fight his military leaders and other conservatives including Thatcher when it came to negotiating nuclear weapons with the Soviets