from Baka-Updates:

Kuzumi Kentarou is a salesman and also a organ donor card owner (their organs get donated upon death). He gets mugged and almost dies but eventually regains consciousness in a hospital and sees a patient with an ailing heart, Hasegawa Kirin, who tells him that he is completely compatible with her... as a donor.

Kentarou promises to give his heart to her. However, Kentarou lives on, but he never got into college. He now works part-time in the hospital where he begs Kisaragi Ryouko, an organ transplant coordinator, "when will Kirin receive his heart?"