We show that the spectral broadening of the pump pulse through self-phase modulation in a time-domain distributed Brillouin sensor has a considerably detrimental effect in the measurement, especially in the case of long distances and high-resolution pulses. Using 30 ns pump pulses with peak power of 276 mW, self-phase modulation leads to a doubling of the effective gain linewidth after some 20 km, which is equivalent to a contrast loss of 2dB in the measurement. The impact is higher for shorter pulses (higher resolution). The theoretical modeling is fully confirmed by experimental results.