Static nonlocal dielectric response of a polar liquid with linearly coupled polarization and density fluctuations is studied. We use a simple quadratic Landau-Ginzburg Hamiltonian to show that the symmetry of interaction between density and vectorial polarization might lead to a striking enhancement of the polarizability at a certain finite wavelength. A similar effect in water has been obtained in recent computer simulations in accordance with neutron diffraction data and predicted by molecular theories. Here, we suggest that the coupling between density and polarization fluctuations might be one of the sources of this behaviour and discuss the conditions for its realization. A closed-form expression is derived for the wave-vector (k-) dependent response function and compared with computer simulation and diffraction data. The expression may be used as a simple analytical framework for describing dielectric screening in polar liquids. Implications of the resonance shape of the response function in k-space are studied for the interionic mean force potential and for the reorganization energy of electron exchange reactions between two ions.