  We propose a theory of longitudinal resistivity in the normal phase of
quasi-one-dimensional organic superconductors near the quantum critical point
where antiferromagnetism borders with superconductivity under pressure. The
linearized semi-classical Boltzmann equation is solved numerically, fed in by
the half-filling electronic umklapp scattering vertex as derived from one-loop
renormalization group calculations for the quasi-one-dimensional electron gas
model. The momentum and temperature dependence of umklapp scattering has an
important impact on the behaviour of longitudinal resistivity in the the normal
phase. Resistivity is found to be linear in temperature around the quantum
critical point at which spin-density-wave order joins superconductivity along
the antinesting axis, to gradually evolve towards the Fermi liquid behaviour in
the limit of weak superconductivity. A comparison is made between theory and
experiments performed on the (TMTSF)$_2$PF$_6$ member of the Bechgaard salt
series under pressure.
