The influence of one or several infrared laser pulses on the stability of bare and argon-tagged sodium chloride clusters is investigated theoretically by a combination of computational methods involving explicit molecular dynamics and properly calibrated unimolecular rate theories. The fragmentation spectra obtained by varying the laser frequency in the far-IR range is compared to the linear absorption spectrum resulting from the dipole moment autocorrelation function. Under appropriate laser field parameters, the action spectra are found to resemble the absorption spectra quite accurately in terms of positions, line widths, and even relative intensities. However, the action spectra exhibit residual and systematic redshifts of a few percent, which are partly due to the finite spectral bandwidth but are amplified by the progressive heating by the laser. A quantitative analysis suggests that these anharmonicity effects should generally arise upon multiple photon absorption.