Scholars and critics alike agree that the "overwhelming question" that is the focus of all of Prufrock's ponderings in the poem is most likely a marriage proposal, or a question of a woman's feelings for him. He obviously cares for a woman, is intimidated by her, has spent time with her, and wants to speak his heart to her. He either wants to propose and get an answer, or to reveal his love for her and have her reveal how she feels for him.
