Final answer:
President Truman requested that Congress approve military intervention if striking workers refused to return to work in a vital industry for national security.
Step-by-step explanation:
In the event that striking workers in an industry deemed essential to national security refused a presidential order to return to work, President Harry Truman requested that Congress take action. According to historical records, the action Truman requested was for Congress to approve military intervention. This would involve the military stepping in to enforce the order and ensure the smooth running of the industry, thus addressing national security concerns. It is important to note that this answer is specific to the scenario in question, and historical events may vary.