The possibility of accelerating electrons to the GeV level using a Petawatt laser focused in a uniform plasma is investigated. The proposed scheme relies on the wakefield acceleration of an electron bunch from a state-of-the-art radio-frequency accelerator. Using an analytical model as well as numerical simulations performed with WAKE [ P. Mora and T. M. Antonsen, Phys. Plasmas 4, 217 (1997) ], a systematical study of the injector parameters is carried out. In particular, it is found that the quality of the accelerated electron bunch—in terms of bunch length and energy spread—depends crucially on the injection energy. Injection energies of a few MeV lead to a GeV electron beam with sub-100 fs bunches and 10% energy spreads. Most of the features of the acceleration process can be explained within the linear response framework, including both the reduction of energy spread and bunch length at low injection energies. The role of nonlinear effects is discussed.