We propose a universal Graph Neural Network architecture which can be trained as an end-2-end search heuristic for any Constraint Satisfaction Problem (CSP). Our architecture can be trained unsupervised with policy gradient descent to generate problem specific heuristics for any CSP in a purely data driven manner. The approach is based on a novel graph representation for CSPs that is both generic and compact and enables us to process every possible CSP instance with one GNN, regardless of constraint arity, relations or domain size. Unlike previous RL-based methods, we operate on a global search action space and allow our GNN to modify any number of variables in every step of the stochastic search. This enables our method to properly leverage the inherent parallelism of GNNs. We perform a thorough empirical evaluation where we learn heuristics for well known and important CSPs, both decision and optimisation problems, from random data, including graph coloring, MAXCUT, and MAX-k-SAT, and the general RB model. Our approach significantly outperforms prior end-2-end approaches for neural combinatorial optimization. It can compete with conventional heuristics and solvers on test instances that are several orders of magnitude larger and structurally more complex than those seen during training.