Highly collimated, quasimonoenergetic multi-MeV electron bunches were generated by the interaction of tightly focused, 80-fs laser pulses in a high-pressure gas jet. These monoenergetic bunches are characteristic of wakefield acceleration in the highly nonlinear wave breaking regime, which was previously thought to be accessible only by much shorter laser pulses in thinner plasmas. In our experiment, the initially long laser pulse was modified in underdense plasma to match the necessary conditions. This picture is confirmed by semianalytical scaling laws and 3D particle-in-cell simulations. Our results show that laser-plasma interaction can drive itself towards this type of laser wakefield acceleration even if the initial laser and plasma parameters are outside the required regime.