The photoabsorption cross section of small sodium and lithium clusters is computed in the time-dependent local density approximation to density functional theory, making use of two different types of ab initio nonlocal pseudopotentials. The equilibrium geometries of the clusters have been obtained via Langevin quantum molecular dynamics. It is found that the average bond length of the clusters and their static polarizabilities depend on the input pseudopotential. Nonetheless, it is found that the different pseudopotentials lead to the same equilibrium shape for the clusters, and to multipeaked line shapes for the photoabsorption cross sections which are nearly identical, apart from small overall energy shifts. For sodium, it is found that the local reduction of the pseudopotential obtained by keeping only its s-part provides, in all cases, an excellent approximation to the full pseudopotential, whereas for lithium the same procedure proves inaccurate.