A variational approach, based on a quadratic trial Hamiltonian is used to determine the configurational as well as the mechanical properties of a system composed of two point charges plus a neutralizing charged polymer, considered as a model of polyelectrolyte–macroion interactions. The quadratic variational ansatz used in the context of charged polymers presents a variant of the Feynman–Kleinert approach properly generalized to include polymer self-interactions. Conditions for chain localization in the field of a point charge are derived and its consequences for polymer-mediated forces between two point charges are analyzed. It is established that in three dimensions the polymer can confer long range attraction to nominally equally charged point ions. At small separations, the polymer mediated force is elastic in origin, stemming from the soft electrostatic anchoring of the chain to both point charges, but with a force constant much stronger than expected from entropic elasticity alone. At large separations, the polymer mediated interactions are of long range and are due to polymer-induced charge reversal on one of the external point charges.