The relocation of the Capital City of Nusantara (IKN) has triggered extensive public opinion dynamics on the X (Twitter) social media platform. This study aims to empirically map public sentiment and evaluate the comparative performance of classification machine learning algorithms: Support Vector Machine (SVM), Logistic Regression (LR), and Multinomial Naïve Bayes (MNB). The dataset comprises 2,257 unique texts spanning the 2024-2025 period, automatically categorized using a lexicon-based approach (InSet dictionary). The technical novelty of this research lies in the extraction of TF-IDF N-gram (1, 2) features, the mitigation of extreme class imbalance via the Synthetic Minority Over-sampling Technique (SMOTE) encapsulated within a cross-validation pipeline, and systematic hyperparameter optimization using GridSearchCV. The labeling results revealed a predominance of negative sentiment at 77.3% (1,745 data) compared to positive sentiment at 22,7% (512 data), reflecting high public scrutiny and skepticism. Based on the model evaluation, MNB with parameter optimization (α=0.1) emerged as the most robust model, achieving an accuracy of 80.5% and a Macro Precision of 72.3%. The performance of MNB proved capable of outperforming the architectures of LR and SVM, which struggled with multicollinearity and underfitting anomalies in high-dimensional spaces. These findings emphasize that the integration of SMOTE and the MNB algorithm is crucial in overcoming majority class bias and calibrating the limitations of static lexicons to precisely map the polarity of public opinion.