The historically-influential perceptual analogy states that intuitions and perceptual experiences are alike in many important respects. Phenomenalists defend a particular reading of this analogy according to which intuitions and perceptual experiences share a common phenomenal character. The phenomenalist thesis has proven highly influential in recent years. However, insufficient attention has been given to the challenges that the phenomenalist thesis raises for theories of intuitions. In this paper, I first develop one such challenge. I argue that if we take seriously the idea that intuitions and perceptual experiences have a common phenomenal character, then an analogous version of the familiar problem of perceptual presence arises for intuitions. I call this the 'problem of intuitive presence'. In the second part of the paper I sketch a novel enactivist solution to this problem.