We investigate the mechanical properties of several model liquids and corresponding local energy minima (inherent structures) in an attempt to explore their connection to slow dynamics and vitrification. In particular, we study the correlation between the distribution of forces between particles and the glass transition in a variety of liquids (with both attractive and repulsive interactions), including network forming liquid silicon, and silica. Such a correlation has been proposed, in analogy with granular materials, within the framework of a unified "jamming phase diagram" and has been studied for some model liquids through simulations recently. We postulate that the plateau behavior at low forces is related to the fragility of the glass former, and provide preliminary supporting evidence. We also consider the critical strain amplitude needed to cause inherent structure transitions and show that the critical strain correlates with the depth of the local energy minima and the onset of slow dynamics.