Many biomineral crystals form complex non-equilibrium shapes, often via transient amorphous precursors. Also in vitro crystals can be grown with non-equilibrium morphologies, such as thin films or nanorods. In many cases this involves charged polymeric additives that form a polymer-induced liquid precursor (PILP). Here, we investigate the CaCO3 based PILP process with a variety of techniques including cryoTEM and NMR. The initial products are 30-50 nm amorphous calcium carbonate (ACC) nanoparticles with ~2 nm nanoparticulate texture. We show the polymers strongly interact with ACC in the early stages, and become excluded during crystallization, with no liquid-liquid phase separation detected during the process. Our results suggest that "PILP" is actually a polymer-driven assembly of ACC clusters, and that its liquid-like behavior at the macroscopic level is due to the small size and surface properties of the assemblies. We propose that a similar biopolymer-stabilized nanogranular phase may be active in biomineralization.