Complex aqueous mixtures comprised of swelling clays and hydrosoluble polymers naturally occur in soils and play a major role in pedogenesis. They are also very often used for formulating oil-well drilling fluids, paints, and personal-care products. The suspensions of some natural clays, thanks to their large nanoparticle aspect ratio, spontaneously form nematic liquidcrystalline phases where the particles align parallel to each other, which affects their flow properties. We observed that adding small amounts of hydrosoluble polymers to these clay suspensions destabilizes the nematic phase with respect to the isotropic (disordered) phase. The polymers that we used (poly(ethylene oxide) and dextran) were too small to adopt particle-bridging conformations and small-angle X-ray scattering experiments showed that the structure of the nematic phase is not altered by polymer doping. However, the adsorption isotherm shows that the macromolecules adsorb onto the clay nanosheets, effectively coating them with a polymer layer. Our extension of Onsager's theory for polymer-coated platelets properly captures the experimental phase diagram and shows how the nematic phase destabilization can be due to the polymer adsorbing more on the platelet faces than at the rim. Because the flow properties of the nematic phase are very different from those of the isotropic phase, the presence or absence of the former phase is an important factor to be determined and considered to explain the rheological behavior of these complex systems.