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Social media users, including organizations, often struggle to acquire the maximum number of responses from other users, but predicting the responses that a post will receive before publication is highly desirable. Previous studies have analyzed why a given tweet may become more popular than others, and have used a variety of models trained to predict the response that a given tweet will receive. The present research addresses the prediction of response measures available on Twitter, including likes, replies and retweets. Data from a single publisher, the official US Navy Twitter account, were used to develop a feature-based model derived from structured tweet-related data. Most importantly, a deep learning feature extraction approach for analyzing unstructured tweet text was applied. A classification task with three classes, representing low, moderate and high responses to tweets, was defined and addressed using four machine learning classifiers. All proposed models were symmetrically trained in a fivefold cross-validation regime using various feature configurations, which allowed for the methodically sound comparison of prediction approaches. The best models achieved F1 scores of 0.655. Our study also used SHapley Additive exPlanations (SHAP) to demonstrate limitations in the research on explainable AI methods involving Deep Learning Language Modeling in NLP. We conclude that model performance can be significantly improved by leveraging additional information from the images and links included in tweets.