Despite many attempts to use ionic liquid media with dissolved lithium salts as the electrolyte component of electrochemical cells, there has been only limited success. Despite its small size, Li+ seems to be the slowest species in the electrolyte, so the cells polarize. As sodium batteries gain attention, the needed Na+-containing ionic liquid electrolytes are likely to encounter similar, but more serious, kinetic problems. Here we first review past attempts to use, as an alternative, inorganic salts and quasi-salts of high conductivity, where conductivity increases with alkali content. Then we provide a detailed study of one organic cation system which confirms and extends earlier work by the Wilkes laboratory that showed how the opposite trend applied for mixtures of NaAlCl4 with the ionic liquid ethylmethylimidazolium tetrachloroaluminate [EMI][AlCl4]. In the present work the depression of conductivity for the Na+ case is fully characterized and is discussed in terms of a 1983 coulomb field alkali trapping concept for low-melting mixtures. This itself is an adaptation of earlier molten salt electrostatic and ionic polarizability models. The apparent exceptionalism of lithium salts in inorganic quasi-ionic liquid solutions is reviewed and possible ways of sidestepping the identified problems for sodium ion conductors are considered. (C) 2014 The Electrochemical Society. All rights reserved.