Filamentation of high-power femtosecond optical pulses in high-pressure gases has gained increasing academic and practical interest from the viewpoint of studying large-scale spectral and temporal transformations occurring with pulsed laser radiation and obtaining super-broadened spectra and extremely short (attosecond) wave packets. Experimentally and theoretically, for the first time to the best of our knowledge, we show that as a result of a 45 fs Ti:sapphire laser pulse filamentation in an optical cell filled with pressurized up to 50 bar nitrogen or argon, the pulse spectrum can reach maximally about eightfold broadening. This limiting pulse spectral width is reached at a gas pressure of about 20 bar and with further pressure increase exhibits saturation and even a slight decrease relative to the limiting value. As a possible reason for this finding, we suppose the increase of pulse energy depletion in the self-created plasma at high gas pressure.