This paper develops a generalized framework that allows us to investigate the vulnerability of the power system nonlinear state estimator to false data injection attacks (FDIAs) from the operator's perspective and to initiate some countermeasures. Unlike most existing FDIA methods, which assume a perfect knowledge of the system measurements and topology by a hacker, we derive and analyze the uncertainties for launching successful FDIAs along with their upper bounds. To effectively defend against an FDIA, we propose a robust detector that checks the measurement statistical consistency using a subset of secure PMU measurements. We first show that if these secure PMU measurements are free of bad data while making the system observable, the FDIA is detectable. We then show that detectability is also ensured if these conditions are relaxed while using alternative redundant measurements from short-term nodal synchrophasor predictions together with the robust Huber M-estimator. Numerical simulation results on the IEEE 30-bus and 118-bus systems demonstrate the effectiveness and robustness of the proposed method even the secure measurements contain noise and bad data.