We consider the Cauchy problem for an energy supercritical nonlinear wave equation that arises in -dimensional Yang-Mills theory. A certain self-similar solution of this model is conjectured to act as an attractor for generic large data evolutions. Assuming mode stability of , we prove a weak version of this conjecture, namely that the self-similar solution is (nonlinearly) stable. Phrased differently, we prove that mode stability of implies its nonlinear stability. The fact that this statement is not vacuous follows from careful numerical work by BizoA" and Chmaj that verifies the mode stability of beyond reasonable doubt.