We suggest to exploit dielectric-metal core-shell nanostructures for efficient resonant and yet broadband absorption of infrared radiation with deeply subwavelength configurations. Realizing that nanostructures would efficiently absorb radiation only when their dielectric properties match those of the environment and making use of the effective medium approach, we develop the design strategy using core-shell nanostructures with very thin shells made of poor metals, i.e., metals having real and imaginary parts of their dielectric permittivities of the same order of magnitude. Analyzing in detail spherical and cylindrical core-shell nanostructures, we demonstrate that the resonant infrared absorption can be not only very efficient, i.e., with the absorption cross sections exceeding geometrical ones, but also broadband with the spectral width being of the order of the resonant wavelength. We obtain simple analytical expressions for the absorption resonances in spherical and cylindrical configurations that allow one to quickly identify the configuration parameters ensuring strong infrared absorption in a given spectral range. Relations to effective medium parameters obtained by the internal homogenization are established and discussed. We believe that our results can be used as practical guidelines for realization of efficient broadband infrared absorbers of subwavelength sizes desirable in diverse applications.