More recent examples underscore the limitations of contempt citations, though. In 2012, Attorney General Eric Holder was held in contempt of Congress for refusing to turn over papers related to a botched operation where illegal guns were sold to people who were thought to be connected to Mexican drug cartels. Holder left office in 2014 with a relatively low approval rating and the Obama administration eventually turned over the documents after a lengthy court battle, but Holder wasn’t prosecuted or forced to resign, and Kriner said the overall political impact was minimal as the investigation wasn’t covered widely in the media, even after Holder was held in contempt.

While Kriner and Schickler’s research has found that prolonged investigations can drag down presidential approval ratings, the fact that recent presidents’ favorability numbers have stayed pretty steady over time could mean that congressional investigations are less likely to have an impact — if nothing seems to affect approval ratings anymore, it may indicate that voters’ opinions are essentially fixed and a congressional investigation may not be enough to move them. This is particularly true for Trump, whose approval ratings are much lower than those of many other presidents. But even if it’s unlikely that holding Barr in contempt will pull Trump’s approval numbers down, that doesn’t mean the citation can’t be a weapon, Schickler said — it just might inflict a different kind of damage. “The risk for the Democrats with all of these investigations is that public interest wanes,” he said. “Because a contempt vote is dramatic, it can drive and sustain public attention on this idea of a lack of transparency and cooperation from the administration, and make it look like the Democrats are taking action.”