  We establish fundamental upper bounds on the electron-phonon interaction
strength and superconducting transition temperature $T_c$ in metals stemming
from an intrinsic instability of the equilibrium between electrons and the
crystal lattice with respect to strong interaction. Our theory explains why the
largest observed electron-phonon couplings $\lambda\le 4$ as well as the
mechanism of metastable superconductivity with higher $T_c$. We conclude based
on our theory and analysis of experimental data that room-temperature
superconductivity is feasible but only in hydrogen compounds.
