Among colossal magnetoresistive manganites the prototypical ferromagnetic manganite La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ has a relatively small magnetoresistance, and has been long assumed to have only weak electron-lattice coupling. Here we report that La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ has strong electron-phonon coupling: Our neutron and x-ray scattering experiments show strong softening and broadening of transverse acoustic phonons on heating through the Curie temperature T$_C$ = 350 K. Simultaneously, we observe two phases where metallic resistivity and polarons coexist. The ferromagnetic polaronic metal phase between 200 K and T$_C$ is characterized by quasielastic scattering from dynamic CE-type polarons with the relatively short lifetime of $mathbf{tau}approx 1,rm{ps}$. This scattering is greatly enhanced above T$_C$ in the paramagnetic polaronic metal phase. Our results suggest that the strength of magnetoresistance in manganites scales with the inverse of polaron lifetime, not the strength of electron-phonon coupling.
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