The viscoelastic response of a binary mixture in the dense supercooled state is studied close to the dynamic transition point of the self-consistent mode-coupling theory. Relaxation of the transverse current correlation functions for the isotropic liquid shows a crossover from the propagating shear waves to diffusive shear mode at a critical wave number q(0). q(0) decreases with increasing density indicating growing correlations, similar to what is observed in computer simulation studies of the same systems. Anomalous stretching of the frequency-dependent shear modulus G(omega) with density is also observed.