In this paper, we present TabSketchFM, a neural tabular model for data discovery over data lakes. First, we propose novel pre-training: a sketch-based approach to enhance the effectiveness of data discovery in neural tabular models. Second, we finetune the model for identifying unionable, joinable, and subset table pairs and show significant improvement over previous tabular neural models. Third, we use these finetuned models to perform table search; i.e., given a query table, find other tables in a corpus that are unionable, joinable, or that are subsets of the query. Our results demonstrate significant improvements for search compared to state-of-the-art techniques. Finally, we show significant transfer across datasets and tasks establishing that our model can generalize across different tasks and over different data lakes.