Final answer:
The patient's symptoms suggest the most likely diagnosis is septic shock, which is associated with arterial and venous dilatation, decreased systemic vascular resistance, and an inflammatory response to infection.
Step-by-step explanation:
The most likely diagnosis for a patient in the intensive care unit with a blood pressure of 87/39, warm, flushed skin, sudden decline in level of consciousness, and with arterial and venous dilatation along with a decrease in systemic vascular resistance is septic shock. Septic shock is characterized by a widespread bacterial infection that causes an inflammatory response throughout the body, leading to the aforementioned symptoms. It typically requires treatment with antibiotics, fluid replacement, and pressor agents to restore vascular tone.