We identify and characterize compact dwarf starburst (CDS) galaxies in the REsolved Spectroscopy Of a Local VolumE (RESOLVE) survey, a volume-limited census of galaxies in the local Universe, to probe whether this population contains any residual `blue nuggets,' a class of intensely star-forming compact galaxies first identified at high redshift z. Our 50 low-z CDS galaxies are defined by dwarf masses (stellar mass M* < 109.5 M circle dot), compact bulged-disc or spheroid-dominated morphologies (using a quantitative criterion, mu (Delta) > 8.6), and specific star formation rates (SSFRs) above the defining threshold for high- z blue nuggets (log SSFR [Gyr-1] > -0.5). Across redshifts, blue nuggets exhibit three defining properties: compactness relative to contemporaneous galaxies, abundant cold gas, and formation via compaction in mergers or colliding streams. Those with halo mass below Mhalo similar to 1011.5 M circle dot may in theory evade permanent quenching and cyclically refuel until the present day. Selected only for compactness and starburst activity, our CDS galaxies generally have Mhalo similar to 1011.5 M similar to and gas-to-stellar mass ratio similar to 1. Moreover, analysis of archival DECaLS photometry and new 3D spectroscopic observations for CDS galaxies reveals a high rate of photometric and kinematic disturbances suggestive of dwarf mergers. The SSFRs, surface mass densities, and number counts of CDS galaxies are compatible with theoretical and observational expectations for redshift evolution in blue nuggets. We argue that CDS galaxies represent a maximally starbursting subset of traditional compact dwarf classes such as blue compact dwarfs and blue E/S0s. We conclude that CDS galaxies represent a low-z tail of the blue nugget phenomenon formed via a moderated compaction channel that leaves open the possibility of disc regrowth and evolution into normal disc galaxies.