The realization of mesoscopic media that mimic an ideal continuous indefinite material remains a challenging problem, particularly because current designs are plagued by spatial dispersion effects and are based on inclusions whose size may be a significant fraction of the wavelength. Here we show that a structure formed by an array of inductively loaded metallic rods terminated by metallic patches at both ends may enable to largely overcome these problems, and imitate more closely indefinite dielectric media with a local response. In particular, we report a strong all-angle negative refraction effect, even in scenarios where the characteristic size of the material is deeply subwavelength. The response of the proposed structure is characterized using a homogenization model developed for the uniaxial wire medium with impedance loadings.