The progressive onset of slip at the wall, which corresponds to a slip length increasing with the solicitation time before reaching a plateau, has been investigated for model viscoelastic polymer solutions, allowing one to vary the longest relaxation time while keeping constant solid-fluid interactions. A hydrodynamic model based on a Maxwell fluid and the classical Navier's hypothesis of a linear response for the friction stress at the interface fully accounts for the data. In the limit of the linear viscoelasticity of the fluid, we could postulate a Newtonian response for the interfacial friction coefficient, reflecting the local character of solid-liquid friction mechanisms. Deviations between the experiments and our model are observed when the fluid is far from its linear viscoelastic behavior.