  Based on recently proposed anti-ferromagnetic spin fluctuation exchange
models for $d_{x^2-y^2}$-superconductors, we show that coupling to harmonic
phonons {\it{cannot}} account for the observed isotope effect in the cuprate
high-$T_c$ materials, whereas coupling to strongly anharmonic multiple-well
lattice tunneling modes {\it{can}}. Our results thus point towards a strongly
enhanced {\it{effective}} electron-phonon coupling and a possible break-down of
Migdal-Eliashberg theory in the cuprates.
