Not all of the electrons in a conductor are mobile, and not all can fit around the attractive charge.
Work Step by Step
Inside a conductor, only a small fraction of the electrons are mobile. For example, a copper atom has 29 electrons, but only 1 or 2 from each atom are free to roam. Furthermore, not all of the free electrons even move toward the charged rod. The ones that get there first clump up, causing an excess of negative charge that repels other electrons.