A longstanding goal in cellular mechanobiology has been to link dynamic biomolecular processes underpinning disease or morphogenesis to spatio-temporal changes in nanoscale mechanical properties such as viscoelasticity, surface tension, and adhesion. This requires the development of quantitative mechanical microscopy methods with high spatio-temporal resolution within a single cell. The Atomic Force Microscope (AFM) can map the heterogeneous mechanical properties of cells with high spatial resolution, however, the image acquisition time is 1-2 orders of magnitude longer than that required to study dynamic cellular processes. We present a technique that allows commercial AFM systems to map quantitatively the dynamically changing viscoelastic properties of live eukaryotic cells at widely separated frequencies over large areas (several 10's of microns) with spatial resolution equal to amplitude-modulation (AM-AFM) and with image acquisition times (tens of seconds) approaching those of speckle fluorescence methods. This represents a ~20 fold improvement in nanomechanical imaging throughput compared to AM-AFM and is fully compatible with emerging high speed AFM systems. This method is used to study the spatio-temporal mechanical response of MDA-MB-231 breast carcinoma cells to the inhibition of Syk protein tyrosine kinase giving insight into the signaling pathways by which Syk negatively regulates motility of highly invasive cancer cells.