Sensors such as phasor measurement units (PMUs) endowed with GPS receivers are ubiquitously installed providing real-time grid visibility. A number of PMUs can cooperatively enable state estimation routines. However, GPS spoofing attacks can notably alter the PMU measurements, mislead the network operator, and drastically impact subsequent corrective control actions. Leveraging a novel measurement model that explicitly accounts for the GPS spoofing attacks, this paper formulates an optimization problem to identify the most vulnerable PMUs in the network. A greedy algorithm is developed to solve the aforementioned problem. Furthermore, the paper develops a computationally efficient alternating minimization algorithm for joint state estimation and attack reconstruction. Numerical tests on IEEE benchmark networks validate the developed methods.