Supervised machine learning algorithms, while popular for sentiment analysis, face limitations tied to the quantity and quality of the training data, especially in the presence of biases or insufficient data. In this study, we try to address these issues investigating the impact of Covid-19 on the Social Mood on Economy Index (SMEI), through a bidirectional long-short term memory (BiLSTM) classifier, computing a daily sentiment index for Italian tweets with economic content throughout 2020 (comprising over 11 million Tweets). We show that training the model with labeled Covid-related Tweets improves the classifier accuracy, while quantitative analysis reveals a sharper decrease in the level of the index during the first lockdown period. Additionally, we explore the effects of different training and tuning procedures, including training set balancing and one-step and two-step approach-es with fine-tuning, on the dynamics of the index. We conclude that, when the size of the training data is small compared to the corpus, it is preferable to perform a one-step training procedure, while balancing the training sets generally improves the model accuracy.