We investigate the electron heating induced by a relativistic-intensity laser pulse propagating through a near-critical plasma. Using particle-in-cell simulations, we show that a specific interaction regime sets in when, due to the energy depletion caused by the plasma wakefield, the laser front profile has steepened to the point of having a length scale close to the laser wavelength. Wave breaking and phase mixing have then occurred, giving rise to a relativistically hot electron population following the laser pulse. This hot electron flow is dense enough to neutralize the cold bulk electrons during their backward acceleration by the wakefield. This neutralization mechanism delays, but does not prevent the breaking of the wakefield: the resulting phase mixing converts the large kinetic energy of the backward-flowing electrons into thermal energy greatly exceeding the conventional ponderomotive scaling at laser intensities >10(21) W cm(-2) and gas densities around 10% of the critical density. We develop a semi-numerical model, based on the Akhiezer-Polovin equations, which correctly reproduces the particle-in-cell-predicted electron thermal energies over a broad parameter range. Given this good agreement, we propose a criterion for full laser absorption that includes field-induced ionization. Finally, we show that our predictions still hold in a two-dimensional geometry using a realistic gas profile.