Best linear unbiased prediction is well known for its wide range of applications including small area estimation. While the theory is well established for mixed linear models and under normality of the error and mixing distributions, the literature is sparse for nonlinear mixed models under nonnormality of the error or of the mixing distributions. This article develops a resampling based unified approach for predicting mixed effects under a generalized mixed model set up. Second order accurate nonnegative estimators of mean squared prediction errors are also developed. Given the parametric model, the proposed methodology automatically produces estimates of the small area parameters and their MSPEs, without requiring explicit analytical expressions for the MSPE.