The sensitivity of electron tunneling to the phase of an ionizing light field is shown to manifest itself in detectable features in the spectral and temporal evolution of intense few-cycle light pulses in an ionizing medium. An ultrafast buildup of electron density in the regime of tunneling ionization gives rise to a modulation of a few-cycle field wave form and enhances the short-wavelength part of its spectrum. In a low-pressure gas, the signatures of electron tunneling in the evolution of few-cycle pulses can be isolated from the effects related to atomic nonlinear susceptibilities, giving an access to attosecond electron tunneling dynamics.