Using three-dimensional particle-in-cell simulations, we show that few-MeV electrons can be produced by tightly focusing few-cycle radially-polarized laser pulses in a low-density atomic gas. In particular, it is observed that for the few-TW laser power needed to reach relativistic electron energies, longitudinal attosecond microbunching occurs naturally, resulting in femtosecond structures with high-contrast attosecond density modulations. The three-dimensional particle-in-cell simulations show that in the relativistic regime the leading pulse of these attosecond substructures survives to propagation over extended distances, suggesting that it could be delivered to a distant target, with the help of a properly designed transport beamline. PACS numbers: 41.75.Jv, 52.38.-r, 61.05.J