We study the constraining power on primordial non-Gaussianity of future surveys of the large-scale structure of the Universe for both near-term surveys (such as the Dark Energy Survey – DES) as well as longer term projects such as Euclid and WFIRST. Specifically we perform a Fisher matrix analysis forecast for such surveys, using DES-like and Euclid-like configurations as examples, and take account of any expected photometric and spectroscopic data. We focus on two-point statistics and consider three observables: the 3D galaxy power spectrum in redshift space, the angular galaxy power spectrum and the projected weak-lensing shear power spectrum. We study the effects of adding a few extra parameters to the basic Λ cold dark matter (ΛCDM) set. We include the two standard parameters to model the current value for the dark-energy equation of state and its time derivative, w0, wa, and we account for the possibility of primordial non-Gaussianity of the local, equilateral and orthogonal types, of parameter fNL and, optionally, of spectral index . We present forecasted constraints on these parameters using the different observational probes. We show that accounting for models that include primordial non-Gaussianity does not degrade the constraint on the standard ΛCDM set nor on the dark-energy equation of state. By combining the weak-lensing data and the information on projected galaxy clustering, consistently including all two-point functions and their covariance, we find forecasted marginalized errors σ(fNL) ∼ 3, from a Euclid-like survey for the local shape of primordial non-Gaussianity, while the orthogonal and equilateral constraints are weakened for the galaxy clustering case, due to the weaker scale dependence of the bias. In the lensing case, the constraints remain instead similar in all configurations.