The present invention provides an apparatus for dispensing rolled sheet material, the apparatus including a housing that defines an interior adapted to rotatably support rolled sheet material and having a dispensing opening sized to allow sheet material to be dispensed therefrom. The apparatus further includes a floating nip within the housing such as, for example, may be formed by first and second rollers. The floating nip minimizes variation in the force required to remove sheet material from the dispenser that may result from a user changing the angle at which sheet material is removed.