We propose a multi-task deep-learning approach for estimating the check-worthiness of claims in political debates. Given a political debate, such as the 2016 US Presidential and Vice-Presidential ones, the task is to predict which statements in the debate should be prioritized for fact-checking. While different fact-checking organizations would naturally make different choices when analyzing the same debate, we show that it pays to learn from multiple sources simultaneously (PolitiFact, FactCheck, ABC, CNN, NPR, NYT, Chicago Tribune, The Guardian, and Washington Post) in a multi-task learning setup, even when a particular source is chosen as a target to imitate. Our evaluation shows state-of-the-art results on a standard dataset for the task of check-worthiness prediction.