We present new sub-arcsecond-resolution Karl G. Jansky Very Large Array (VLA) imaging at 10 GHz of 155 ultra-luminous (\(L_{\rm bol}\sim10^{11.7-14.2} L_\odot\)) and heavily obscured quasars with redshifts \(z \sim0.4-3\). The sample was selected to have extremely red mid-infrared (MIR)-optical color ratios based on data from Wide-Field Infrared Survey Explorer (WISE) along with a detection of bright, unresolved radio emission from the NRAO VLA Sky Survey (NVSS) or Faint Images of the Radio Sky at Twenty-Centimeters (FIRST) Survey. Our high-resolution VLA observations have revealed that the majority of the sources in our sample (93 out of 155) are compact on angular scales \(<0.2^{\prime \prime}\) (\(\leq 1.7\) kpc at \(z \sim2\)). The radio luminosities, linear extents, and lobe pressures of our sources are similar to young radio active galactic nuclei (AGN; e.g., Gigahertz Peaked Spectrum, GPS, and Compact Steep Spectrum, CSS, sources), but their space density is considerably lower. Application of a simple adiabatic lobe expansion model suggests relatively young dynamical ages (\(\sim10^{4-7}\) years), relatively high ambient ISM densities (\(\sim1-10^4\) cm\(^{-3}\)), and modest lobe expansion speeds (\(\sim30-10,000\) km s\(^{-1}\)). Thus, we find our sources to be consistent with a population of newly triggered, young jets caught in a unique evolutionary stage in which they still reside within the dense gas reservoirs of their hosts. Based on their radio luminosity function and dynamical ages, we estimate only \(\sim20\%\) of classical large scale FRI/II radio galaxies could have evolved directly from these objects. We speculate that the WISE-NVSS sources might first become GPS or CSS sources, of which some might ultimately evolve into larger radio galaxies.