When oppositely charged polymers are mixed, counterion release drives phase separation; understanding this process is a key unsolved problem in polymer science and biophysical chemistry, particularly for nucleic acids, polyanions whose biological functions are intimately related to their high charge density. In the cell, complexation by basic proteins condenses DNA into chromatin, and membraneless organelles formed by liquid-liquid phase separation of RNA and proteins perform vital functions and have been linked to disease. Electrostatic interactions are also the primary method used for assembly of nanoparticles to deliver therapeutic nucleic acids into cells. This work describes complexation experiments with oligonucleotides and cationic peptides spanning a wide range of polymer lengths, concentrations, and structures, including RNA and methylphosphonate backbones. We find that the phase of the complexes is controlled by the hybridization state of the nucleic acid, with double-stranded nucleic acids forming solid precipitates while single-stranded oligonucleotides form liquid coacervates, apparently due to their lower charge density. Adding salt "melts" precipitates into coacervates, and oligonucleotides in coacervates remain competent for sequence-specific hybridization and phase change, suggesting the possibility of environmentally responsive complexes and nanoparticles for therapeutic or sensing applications.