  The quasi-1D organic Bechgaard salt (TMTSF)$_2$PF$_6$ displays
spin-density-wave (SDW) order and superconductivity in close proximity in the
temperature-pressure phase diagram. We have measured its normal-state
electrical resistivity $\rho_a(T)$ as a function of temperature and pressure,
in the $T \to 0$ limit. At the critical pressure where SDW order disappears,
$\rho_a(T) \propto T$ down to the lowest measured temperature (0.1 K). With
increasing pressure, $\rho_a(T)$ acquires a curvature that is well described by
$\rho_a(T) = \rho_0 + AT + BT^2$, where the strength of the linear term,
measured by the $A$ coefficient, is found to scale with the superconducting
transition temperature $T_c$. This correlation between $A$ and $T_c$ strongly
suggests that scattering and pairing in (TMTSF)$_2$PF$_6$ have a common origin,
most likely rooted in the antiferromagnetic spin fluctuations associated with
SDW order. Analysis of published resistivity data on the iron-pnictide
superconductor Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ reveals a detailed similarity
with (TMTSF)$_2$PF$_6$, suggesting that antiferromagnetic fluctuations play a
similar role in the pnictides.
