Doped manganese oxides such as La0.67Ca0.33MnO3 (LCMO) are strongly correlated electron systems which display an insulator to metal transition upon cooling at a temperature T_MI. At low temperature the material is ferromagnetic. Above the transition the material is a paramagnetic insulator in which conduction is governed by activated polaron hopping. As yet, the fundamental question of conductance on micrometer length scales (the scale on which electronic phase separation can occur) has been little studied. We investigate this question of electrical transport in LCMO, which requires the fabrication of micron sized structures in LCMO thin films. We measure current-voltage (I-V) characteristics as function of temperature, in high magnetic fields, in electric fields and with varying film thickness. In warming from the metallic to the insulating state we find strong non-linear effects in the steep part of the transition. The differential resistance is largest at zero bias, then drops with increasing current, and saturates at a current density which is the same for different samples. Resistance drops of up to 80 % are observed upon increasing the applied current. We propose that the nonlinear behavior is a direct signature of an intervening phase involving the formation of short range polaron correlations (electron-glass). The nonlinear behavior occurs when the homogeneous glass phase which now encompasses the entire microstructure is melted by the applied electrical current. We also associate the formation of inhomogeneities in the microstructure with the appearance of a strong electric field effect.