  We study the impact of the cosmological parameters uncertainties on the
measurements of primordial non-Gaussianity through the large-scale non-Gaussian
halo bias effect. While this is not expected to be an issue for the standard
LCDM model, it may not be the case for more general models that modify the
large-scale shape of the power spectrum. We consider the so-called local
non-Gaussianity model and forecasts from planned surveys, alone and combined
with a Planck CMB prior. In particular, we consider EUCLID- and LSST-like
surveys and forecast the correlations among $f_{\rm NL}$ and the running of the
spectral index $\alpha_s$, the dark energy equation of state $w$, the effective
sound speed of dark energy perturbations $c^2_s$, the total mass of massive
neutrinos $M_\nu=\sum m_\nu$, and the number of extra relativistic degrees of
freedom $N_\nu^{rel}$. Neglecting CMB information on $f_{\rm NL}$ and scales $k
> 0.03 h$/Mpc, we find that, if $N_\nu^{\rm rel}$ is assumed to be known, the
uncertainty on cosmological parameters increases the error on $f_{\rm NL}$ by
10 to 30% depending on the survey. Thus the $f_{\rm NL}$ constraint is
remarkable robust to cosmological model uncertainties. On the other hand, if
$N_\nu^{\rm rel}$ is simultaneously constrained from the data, the $f_{\rm NL}$
error increases by $\sim 80%$. Finally, future surveys which provide a large
sample of galaxies or galaxy clusters over a volume comparable to the Hubble
volume can measure primordial non-Gaussianity of the local form with a
marginalized 1--$\sigma$ error of the order $\Delta f_{\rm NL} \sim 2-5$, after
combination with CMB priors for the remaining cosmological parameters. These
results are competitive with CMB bispectrum constraints achievable with an
ideal CMB experiment.
