  We investigate the electrical transport in mesoscopic structures of
La$_{0.67}$Ca$_{0.33}$MnO$_3$ in the regime of the metal-insulator transition
by fabricating microbridges from strained and unstrained thin films. We measure
current-voltage characteristics as function of temperature and in high magnetic
fields and with varying film thickness. For strained films, in warming from the
metallic to the insulating state, we find non-linear effects in the steep part
of the transition characterized by a differential resistance with a strong peak
around zero applied current, and saturating at higher currents after resistance
drops up to 60 %. We propose that this nonlinear behavior is associated with
melting of the insulating state by injecting charge carriers, signalling the
occurrence of an intervening phase which involves the formation of short range
polaron correlations.
