We identify and characterize compact dwarf starburst (CDS) galaxies in the 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 $M_* < 10^{9.5}$ M$_{odot}$), compact bulged-disk or spheroid-dominated morphologies (using a quantitative criterion, $mu_Delta > 8.6$), and specific star formation rates 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 $M_{rm halo} sim 10^{11.5}$ M$_{odot}$ 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 $M_{rm halo} lesssim 10^{11.5}$ M$_{odot}$ and gas-to-stellar mass ratio $gtrsim$1. Moreover, analysis of archival DECaLS photometry and new 3D spectroscopic observations for CDS galaxies reveals a high rate of photometric and kinematic disturbances suggestive of dwarf mergers. The SSFRs, surface mass densities, and number counts of CDS galaxies are compatible with theoretical and observational expectations for redshift evolution in blue nuggets. We argue that CDS galaxies represent a maximally-starbursting subset of traditional compact dwarf classes such as blue compact dwarfs and blue E/S0s. We conclude that CDS galaxies represent a low-$z$ tail of the blue nugget phenomenon formed via a moderated compaction channel that leaves open the possibility of disk regrowth and evolution into normal disk galaxies.
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