The contact between semiconducting single-wall carbon nanotubes (SWCNTs) and metallic leads is of central importance to potential electronic device applications. We investigate the nature of the contact of SWCNTs with Pd leads in a fully covered geometry that closely resembles experimental setups. We employ first-principles calculations within density functional theory to obtain the equilibrium structure for representative semiconducting SWCNTs embedded in Pd and analyze their electronic structure features, charge-transfer effects, electrostatic potentials, and Fermi level alignment at the interfaces with the metal contact. We find that there is no electrostatic or Schottky-type barrier to electron transfer between the metal and the nanotube.