We report on the first experimental measurement of the spectral broadening of the harmonic emission associated with only the long electron quantum paths as a function of the driving pulse intensity. For such measurements we have estimated the chirp coefficient associated with the long quantum paths, within the strong-field approximation. This coefficient describes how the harmonic phase depends on the intensity of the driving laser field. The dependence of the chirp coefficient on the driving pulse intensity and on the harmonic order, which strongly influence the characteristics of the harmonic radiation, has been experimentally investigated. The experimental values turn out to be in excellent agreement with the results of numerical simulations based on the use of the nonadiabatic saddle-point method.