Should the House impeach Donald Trump, 67 Senators—or a two thirds majority—must then vote to remove him from office. In practice, this means that 20 Republican senators must go against their own party to boot the president. At present, this seems impossible, or at least highly unlikely. Trump still enjoys the support of a vast majority of Republican voters, which means lawmakers who turn on him would then have to answer to the base. And yet, as the Ukraine scandal trundles on, some of the president’s allies are beginning to fret. “There’s most definitely a group of Republican senators who are not originally Trump fans that have endorsed him begrudgingly, who have warmed up to him as their fortunes rise,” a former senior Trump administration official told Politico. Former 2016 Trump campaign adviser Michael Caputo added, warily, “If there’s one place where you can set a trap that nobody expects, it’s the U.S. Senate Republican Conference.”

Their fears are not unfounded. Recent polling shows that 30% of Republicans are in favor of an impeachment inquiry, while almost one fifth say they favor an impeachment vote. Last month, a GOP consultant said a Republican senator told him that if the vote were secret, “30 Republican senators would vote to impeach Trump.” He noted, “The politics of it will get worse and worse for Trump.”

Of course, the vote is not secret. And as it stands, Trump and his allies are counting on a healthy amount of public shaming and groupthink to keep the caucus in line. The president himself has used a carrot-and-stick approach, doing things like attacking Mitt Romney as a “pompous ass”, and doling out endorsements to senators running for reelection in swing states. (He recently endorsed Ben Sasse, one of his loudest critics, who called Trump’s call with Ukrainian president Volodymyr Zelensky “very troubling.”) He’s also deployed Mike Pence to make appearances, recently with Senator Joni Ernst, who’s up for reelection in Iowa. And yet, it’s not clear that these entreaties are having the intended effect: