Final answer:
The nurse should prioritize assessing the post-vaginal delivery patient with heavy vaginal bleeding, as it indicates a potential postpartum hemorrhage, which is a life-threatening emergency.
Step-by-step explanation:
The nurse should assess the post-vaginal delivery patient with heavy vaginal bleeding first. This situation is indicative of postpartum hemorrhage and is potentially the most life-threatening condition among the options provided. Managing blood loss is critical to prevent the development of hypovolemic shock. The other conditions, such as breast engorgement, abdominal cramping, and incisional pain, while uncomfortable, are not as immediately life-threatening as heavy vaginal bleeding and can be prioritized after.