We combine ab ititio density functional theory with transport calculations to provide a microscopic basis for distinguishing between 'good' and 'poor' metal contacts to nantubes. Comparing Ti and Pd as examples of different contact metals, we trace back the observed superiority of Pd to the nature of the metal-nanotube hybridization. For Pd interacting with nanotubes or graphite, this hybrid state is associated with an inter-layer state, and allows carrier injection with the Fermi momentum of the nanotube. Based on our Landauer-Büuttiker transport results, we furthermore suggest that the 'optimum' metal-nanotube contact combines a weak hybridization with a large contact length between the metal and the nanotube.