Read: Peter Strzok rejects accusations of anti-Trump bias

Other than a cryptic comment during a Senate hearing that he was “looking into” potentially “improper surveillance” of the Trump campaign, there is no indication so far that Barr plans to open such an investigation. But it seems that Republicans will grow only more vocal in their demands for it—at least in part because they think it will help the president politically. On Friday, Trump himself tweeted that it was “finally time to turn the tables and bring justice to some very sick and dangerous people who have committed very serious crimes, perhaps even Spying or Treason.”

Many Republicans in Washington stressed to me that there are substantive things to be gained from an investigation. One senior House Republican aide—who, like others I talked to for this story, spoke on the condition of anonymity in order to be frank—told me it was important to many lawmakers that there be “accountability” for the likes of former FBI Director James Comey, former Deputy Director Andrew McCabe, and the former agent Peter Strzok, whom Republicans have long accused of improperly investigating and surveilling the Trump campaign because of their personal bias. Offering an example, Giuliani told me that an investigation could help determine why George Papadopoulos’s conversation with an Australian diplomat—in which the Trump campaign staffer said he’d learned that Moscow had thousands of Hillary Clinton’s emails—justified launching the Russia probe.

But Giuliani also suggested an alternative motivation that’s gaining a foothold in Republican circles: that an investigation would keep Mueller’s findings alive in a way that’s helpful to the president. When I asked him what investigating the investigators would ideally accomplish, he said, “Getting Jerry Nadler to be a household presence,” referring to the House Judiciary Committee chairman, who is leading one of the congressional inquiries into the president. Giuliani then added, sarcastically, “The more people see Jerry, the more they will love him. He’s so objective.”

Indeed, the more Republicans I spoke to for this story, the more obvious it became that their party’s pleas for Democrats to put Mueller behind them may be little more than lip service. One Trump-campaign adviser said that they are more than happy for Democrats to hold firm and continue broadcasting their opinions about collusion and obstruction.

One former White House official told me that an investigation would allow Trump-campaign staffers to frame their message in much the same way they did in 2016, claiming that “the system is rigged against them.” “Everyone needs a bogeyman, and this gives them something to hang on to,” the former official said. “I don’t know that everyone and their mother knows who Robert Mueller is, but if you told a Trump supporter that Democrats had used phony information to launch an investigation into their guy, it would absolutely fire them up.”