Giuliani, the newest addition to the president's legal team, first rattled the White House last week when he sat for interviews on Fox News and seemed to contradict Trump by saying the president was aware of the $130,000 payout to Daniels from his personal attorney, Michael Cohen. He also suggested the October 2016 settlement had been made because Trump was in the stretch run of his presidential campaign.
After Trump chided Giuliani on Friday, saying the lawyer needed to "get his facts straight," Giuliani put out a statement trying to clarify his remarks. But in weekend interviews, Giuliani appeared to dig himself a deeper hole by acknowledging that "Cohen takes care of situations like this, then gets paid for them sometimes." He did not rule out the possibility that Cohen had paid off other women.
Trump, who has denied the affair with Daniels, was angry that Giuliani had given the impression that other women may have made similar charges of infidelity, according to the people familiar with his views.
Additionally, Trump has grown agitated in recent days by replays of Giuliani's interview with Sean Hannity, in which he said that Trump knew about the payment but that it wasn't a campaign violation. A clearly surprised Hannity then asked, "Because they funneled it through the law firm?"
To which Giuliani responded, "Funneled it through the law firm, and the president repaid him."
Trump snapped at both men in recent days, chiding Hannity for using the word "funneled," which he believes had illegal connotations, according to the people who spoke to The Associated Press. As for Giuliani, the president has not yet signaled to him to stop appearing on television but told a confidant recently that perhaps Giuliani should "be benched" — at least temporarily — if he can't improve his performance.
The president has not publicly discussed dismissing Giuliani and has appreciated his sharp attacks on the Russia investigation and his forceful battles with the press, according to three White House aides and outside allies. The two men have spoken frequently, according to officials familiar with their interactions but not authorized to discuss private conversations.
But many Trump allies both inside and outside the White House have grown anxious in recent days about Giuliani's whirlwind and unpredictable interviews.
"They're admitting to enough that warrants scrutiny. It shouldn't be put on television shows off the cuff," said Alan Dershowitz, the emeritus Harvard law professor who has been informally advising Trump on the Russia collusion probe. "This is not the way to handle a complicated case."
Many in the White House have begun evoking comparisons between Giuliani and Anthony Scaramucci, another hard-charging New Yorker with a knack for getting TV airtime.
Scaramucci lasted 11 days before being fired. The former White House communications director himself drew parallels between his own burn-bright-burn-fast tenure and Giuliani's performance.
"I am enjoying all of the comparisons between me and the mayor #RudyGiuliani," Scaramucci tweeted Sunday. "He is loyal, tough and a fierce competitor. He fights and will win for @realDonaldTrump @POTUS. Big compliment thank you!"
Giuliani did not respond to requests for comment.
West Wing aides were blindsided by Giuliani's TV appearances last week, and many senior advisers and members of the president's legal team have been cut out of the decision-making process. But some aides have been reluctant to broach the subject with Trump because it only increases their liability, according to officials.
Press secretary Sarah Huckabee Sanders, who was among those surprised by Giuliani's string of TV appearances, said Monday that Trump felt the former mayor "added value" to his outside legal team. On Friday, Trump said Giuliani was "a great guy but he just started a day ago." He made clear Giuliani was still "learning the subject matter."
Some West Wing aides have complained that Giuliani, who ran for president in 2008, was acting like a "principal" and not a member of a team. And some in Trump's inner circle raised their eyebrows at Giuliani's declaration that Jared Kushner, the president's son-in-law and senior adviser, was "disposable." He also declined to rule out Trump invoking the Fifth Amendment in special counsel Robert Mueller's ongoing Russia probe.
The episode revived worries in Trump's inner circle about Giuliani, who enjoys the media limelight and has a tendency to go off-script. His behavior grew more unpredictable during the stretch run of the 2016 presidential campaign, when Trump chided him for falling asleep on the campaign plane, according to two former campaign officials who spoke on condition of anonymity to discuss internal matters.
Giuliani also alienated a number of people in Trump's inner circle by insisting that the only Cabinet position he would consider would be secretary of state. He did not get the post.
Giuliani's remarks have also been watched with concern at the State Department and Pentagon after he weighed in recently on international affairs. He declared last week that North Korea would be releasing three Americans being held captive, which has not yet happened, and said the administration was committed to regime change in Iran, a stance Trump has not taken.
"He speaks for himself and not on behalf of the administration on foreign policy," State Department spokeswoman Heather Nauert said Monday.