The microwave sky shows unexpected features at the largest angular scales, among them the alignments of the dipole, quadrupole and octopole. Motivated by recent X-ray cluster studies, we investigate the possibility that local structures at the 100 h^(-1) Mpc scale could be responsible for such correlations. These structures give rise to a local Rees-Sciama contribution to the microwave sky that may amount to Delta T/T ~ 10^(-5) at the largest angular scales. We model local structures by a spherical overdensity (Lemaitre-Tolman-Bondi model) and assume that the Local Group is falling toward the centre. We superimpose the local Rees-Sciama effect on a statistically isotropic, gaussian sky. As expected we find alignments among low multipoles, but a closer look reveals that they do not agree with the type of correlations revealed by the data.