The differential cross section and polarization observables for the elastic reaction induced by deuteron scattering off electrons at rest are calculated in the one-photon-exchange (Born) approximation. Specific attention is given to the kinematical conditions, that is, to the specific range of incident energy and transferred momentum. The specific interest of this reaction is to access very small transferred momenta. Numerical estimates are given for polarization observables that describe the of single- and double-spin effects, provided that the polarization components (both, vector and tensor) of each particle in the reaction are determined in the rest frame of the electron target.