We use ultrashort intense laser pulses to study superconducting state vaporization dynamics in La2-xSrxCuO4 (x=0.1 and 0.15) on the femtosecond time scale. We find that the energy density required to vaporize the superconducting state is 2.0+/-0.8 and 2.6+/-1.0 K/Cu for x=0.1 and 0.15, respectively. This is significantly greater than the condensation energy density, indicating that the quasiparticles share a large amount of energy with the boson glue bath on this time scale. Considering in detail both spin and lattice energy relaxation pathways which take place on the relevant time scale of approximately 10(-12) s, the experiments appear to favor phonon-mediated pair-breaking mechanisms over spin-mediated pair breaking.