After the raid, Mr. Trump decided to double down on his more aggressive strategy, according to people close to him. He hired Mr. Giuliani to replace his lawyer John M. Dowd, who had convinced Mr. Trump of the value of the earlier, more cooperative approach. Mr. Giuliani immediately began a public relations assault on Mr. Mueller. Mr. Flood, who is known for his strong view of the president’s powers to shield his communications and documents from investigators, was brought on in May. 
 
 Mr. Giuliani has sown doubt and confusion by pushing dubious theories about the case. He has made claims like accusing Mr. Mueller’s office, without evidence, of trying to frame Mr. Trump. Mr. Giuliani has also pushed unfounded theories, like an assertion that the F.B.I. implanted a spy in Mr. Trump’s campaign. 
 
 The president and his lawyers have also tried to undermine key witnesses like James B. Comey, the former F.B.I. director fired by Mr. Trump, to force the public to decide whether to believe them or the president. That is a tall task — the president’s penchant for half-truths, exaggerations and outright falsehoods is well established. 
 
 But Mr. Trump and his lawyers contend that Mr. Comey damaged his credibility as a witness during his book tour this spring by showing that he played by his own rules when he ran the F.B.I., and that the findings of a recent inspector general report critical of the F.B.I.’s handling of the Hillary Clinton email investigation buttressed their case. 
 
 Mr. Giuliani views the tactics as an early success. “Right now, public opinion is going in our direction big time,” he said. 
 
 His approach also extends to his public portrayal of the negotiations with Mr. Mueller over a presidential interview. Even as they have delayed any agreement for at least six months of negotiations, the lawyers have condemned the special counsel for dragging out the inquiry, saying he has had more than enough time to complete his investigation. 
 
 Mr. Giuliani has gone back and forth about whether the president will agree to be questioned and given varying timetables. He once said Mr. Trump would make a decision after his meeting with the North Korean leader, Kim Jong-un, last month, then changed that deadline to July. The president’s lawyers have set other deadlines that came and went without resolution. ||||| Rudy Giuliani, Trump’s attorney, is again playing hardball with special counsel Robert Mueller — and it’s looking even less likely that the president will sit down for an interview with Mueller’s team. 
 
 The New York Times’s Michael Schmidt and Maggie Haberman reported that Giuliani is setting new terms for the interview: Mueller must show evidence that Donald Trump committed a crime and that an interview is necessary, or forget it. Trump’s legal team is also insisting Mueller prove that he exhausted all other avenues and that he has no choice but to interview the president. 
 
 “If they can come to us and show us the basis and that it’s legitimate and that they have uncovered something, we can go from there and assess their objectivity,” Giuliani told the Times. 
 
 The prospect of sitting for an interview with Robert Mueller has gotten increasingly fraught since the president shook up his legal team months ago, bringing on former New York City Mayor Rudy Giuliani and Emmet T. Flood, who represented Bill Clinton in his impeachment. Both embarked on a more combative, aggressive approach toward the Russia investigation compared to the more cooperative stance favored by his former attorneys. 
 
 Giuliani has shifted the terms (and deadline) of a Trump-Mueller interview more than once since joining Trump’s legal team. Giuliani had said in May that he was working with the special counsel to narrow the scope of the investigation, and that no decisions would be made until after Trump’s summit with North Korean leader Kim Jong Un. The summit came and went, and the deadline was pushed to July 4. 
 
 The delays on the Mueller interview are part of Team Trump’s attempts to sway public opinion 
 
 As the back-and-forth over the Trump interview continues, Giuliani is waging a PR campaign against Mueller and the investigation that’s been echoed in his boss’s Twitter feed. According to the latest Times report, this seems to be the crux of the strategy — delay until the midterms and damage the investigation’s credibility. (It may also force Mueller to subpoena Trump — which will set off a protracted, likely messy, court battle.) 
 
 Trump’s lawyers have suggested Mueller will abide by Department of Justice guidance that says a sitting president can’t be indicted — which would mean Mueller’s most likely option is a written report, which could make its way to Congress. If such a report is damning against Trump, and if Democrats retake the House of Representatives in the fall, the chance of impeachment increases. But if the public can be convinced, that, as the president says, that the special counsel’s investigation is a total “WITCH HUNT,” lawmakers might be more leery of taking on the president. 
 
 “Nobody is going to consider impeachment if public opinion has concluded this is an unfair investigation, and that’s why public opinion is so important,” Giuliani told the Times. 
 
 Giuliani, Trump, and his allies in Congress have done their best to discredit Mueller. Giuliani played up the debunked “Spygate” conspiracy — that the FBI planted a spy on the Trump campaign — admitting last month that the drama was conjured up “for public opinion.” The House of Representatives is waging war against Deputy Attorney General Rod Rosenstein — Mueller’s boss — sanctioning him on the House floor for failing to turn over requested documented about the investigation. 
 
 The war against Mueller has shown some signs of working. A Politico/Morning Consult poll in June put Mueller’s favorability at just 32 percent. More people — 36 percent — had an unfavorable opinion of Mueller than a favorable one. Opinions have dipped sharply among Republicans, too: According to that same poll, 53 percent of Republicans viewed Mueller unfavorably, up from 27 percent in July 2017, according to Politico. 
 
 The Times also pointed to a Washington Post-Schar School poll, published Friday, that put Mueller’s approval rating at just 49 percent among all adults — though it reached 52 percent among registered voters. A total of 45 percent of adults disapproved of Mueller.
– The White House is changing its posture in the ongoing saga of the Mueller probe. Trump attorney Rudy Giuliani tells the New York Times that the president will sit for an interview with Robert Mueller only if the special counsel can show evidence that Trump committed a crime. "If they can come to us and show us the basis and that it’s legitimate and that they have uncovered something, we can go from there," Giuliani said, acknowledging that it's not likely Mueller will agree to the new conditions. However, as the Times notes, it remains possible for Mueller to subpoena Trump in his bid to uncover any links between Russia and the Trump presidential campaign. According to Vox, Giuliani's move is part of team Trump's increasingly combative stance against the special counsel. Part of that strategy involves a PR campaign to paint the investigation as an unfair assault on Trump. Should such a campaign successfully sway public opinion, congressional action against Trump would be less likely should Mueller's report cast the president in an unflattering—or, possibly, impeachment-worthy—light. To the Times, Giuliani openly admits this strategy. “Nobody is going to consider impeachment if public opinion has concluded this is an unfair investigation, and that’s why public opinion is so important,” he said.