The origin of supersonic infrared and radio recombination nebular lines often detected in young and massive superstar clusters is discussed. We suggest that these arise from a collection of repressurizing shocks (RSs), acting effectively to re-establish pressure balance within the cluster volume and from the cluster wind which leads to an even broader although much weaker component. The supersonic lines here are shown to occur in clusters that undergo a bimodal hydrodynamic solution, that is within clusters that are above the threshold line in the mechanical luminosity or cluster mass versus the size of the cluster plane. A plethora of RSs is due to frequent and recurrent thermal instabilities that take place within the matter reinserted by stellar winds and supernovae. We show that the maximum speed of the RSs and of the cluster wind are both functions of the temperature reached at the stagnation radius. This temperature depends only on the cluster heating efficiency (η). Based on our two-dimensional simulations we calculate the line profiles that result from several models and confirm our analytical predictions. From a comparison between the predicted and observed values of the half-width zero intensity of the two line components, we conclude that the thermalization efficiency in young super star clusters above the threshold line must be lower than 20%.