Accurate estimation of the duration of soft-x-ray pulses from high-harmonic generation (HHG) remains challenging given their higher photon energies and broad spectral bandwidth. The carrier-envelope-phase (CEP) dependence of generated soft-x-ray spectra is indicative of attosecond pulse generation, but advanced simulations are needed to infer the pulse duration from such data. Here, we employ macroscopic propagation simulations to reproduce experimental polarization-gated CEP-dependent soft-x-ray spectra. The simulations indicate chirped pulses, which we theoretically find to be compressible in hydrogen plasmas, suggesting this as a viable compression scheme for broadband soft-x-rays from HHG.