Rudy Giuliani's latest media blitz, which was filled with a dizzying array of misstatements and hurried clarifications, agitated President Donald Trump and some of his allies, who have raised the possibility that the outspoken presidential lawyer should be sidelined from televised interviews – at least temporarily.

'Every time he opens his mouth on TV it's like "Cleanup on aisle Giuliani!"' a White House official told DailyMail.com on Wednesday.

Politico reported that a White House official acknowledged the severity of the West Wing's all-hands approach to putting out Giuliani-related fires.

'Handling Rudy’s f*** ups takes more than one man,' that official said.

Trump was frustrated with Giuliani, according to three White House officials and Republicans close to the White House who were not authorized to speak publicly about private conversations.

Yet the president is in no mood to cut him loose, according to CNN. 'Rudy's not getting fired,' one of the network's sources said.

Some of Trump's allies have suggested that Giuliani should at least be barred from evening interviews because of concerns that he was going on TV after drinking, according to three Republicans close to the White House.

Rudy Giuliani's scattershot media blitzes, filled with a dizzying array of wild misstatements, hurried clarifications and eyebrow-raising assertions, have agitated President Donald Trump and some of his allies

President Trump's ides say it takes more than one person at the White House to manage the fallout from Giuliain's 'f*** ups' and that 'every time he opens his mouth on TV it's like "Cleanup on aisle Giuliani!"'

Giuliani has previously insisted he does not have an issue with alcohol, denying to Politico last May that it affected his interviews. He added: 'I may have a drink for dinner. I like to drink with cigars.'

White House Press Secretary Sarah Sanders walked away from reporters on Wednesday morning outside the West Wing when she was asked about Giuliani.

The president told advisers that he felt his lawyer had obscured what he believed was a public relations victory: the special counsel's rare public statement disputing portions of a BuzzFeed News story that Trump instructed his former attorney, Michael Cohen, to lie before Congress.

The president told confidants that Giuliani had 'changed the headlines' for the worse and raised the possibility that Giuliani do fewer cable hits, at least for a while, according to the officials and Republicans.

Several of Trump's influential outside allies also have begun expressing reservations about Giuliani. Some members of this informal network of advisers, whom the president frequently calls from the White House residence, urged Trump in recent days to bench Giuliani – but most stopped short of suggesting he fire his trusted attorney.

Not going there: White House Press Secretary walked away from reporters on Wednesday when they asked her about Giuliani

Rarely reluctant to appear before TV cameras or answer a reporter's call, Giuliani has spent nearly a year acting as a sort of human smokescreen for Trump. He has long played the role more of presidential spokesman than attorney, often unleashing public attacks on special counsel Robert Mueller's probe into possible contacts between the Trump campaign and Russia.

But a recent set of interviews, which were quickly pilloried across cable news, prompted increased concerns about both Trump's legal exposure and the effectiveness of his vocal attorney.

Frustration about Giuliani in the West Wing has long run rampant. The former New York City mayor, who frequently speaks directly to the president, is Trump's outside counsel and works in a different orbit than White House officials, who are still left to play damage control after some of Giuliani's wilder interviews.

The latest furor began Sunday as Giuliani, wearing a suit, tie and New York Yankees World Series ring, appeared on NBC's 'Meet the Press' and dramatically altered the timeline regarding discussions about a Trump Tower in Moscow, now asserting they stretched until November 2016.

That statement, which suggested that the Trump Organization was engaged in business dealings with Russia up to and beyond the election, ignited a firestorm and then an abrupt walk-back from Giuliani.

Hard to handle: Some Trump allies fear that Giuliani creates problems by shooting from the hip on TV because he drinks before he goes on the air; Giuliani insists there's no problem

He issued a statement the next day saying his comments about the project 'were hypothetical and not based on conversations I had with the President. My comments did not represent the actual timing or circumstances of any such discussions.'

Then, hours later in an interview with The New Yorker, Giuliani raised eyebrows again when he seemed to suggest he had listened to tapes of Trump and Cohen that had not previously been discussed.

'I shouldn't have said tapes,' Giuliani said as he tried to backtrack. He then added that there were 'No tapes. Well, I have listened to tapes, but none of them concern this.' He did not elaborate further.

The muddled interviews were a failed victory lap over the BuzzFeed story, which prompted a number of House Democrats to raise the possibility of impeaching Trump. But the special counsel, which rarely issues public responses, said that at least portions of the story were not accurate, leading both Giuliani and Trump to crow about media bias against the Republican president.

BuzzFeed has issued statements standing by its reporting. No other media outlet has confirmed the story. Giuliani did not immediately respond to a request for comment Tuesday.

This is far from the first time Giuliani has been forced to issue a clarification, as he has frequently offered contradictory accounts of developments in the Russia investigation.

Earlier this month, he was forced to clean up a remark in which he asserted that he only could vouch that the president had not colluded with Russia, rather than the whole campaign, a dramatic change of story.

'Rudy had done a very good job going on TV and fighting back and laying down a defense of the president,' said Sam Nunberg, a former low-level Trump campaign aide who left on bad terms in 2015.

'But now it's time to get precise, you can't be so loose anymore. He had a major slip.'

Trump has no plan to fire Giuliani, according to people in his inner circle

At times, Giuliani's seemingly out-of-nowhere admissions in interviews have, in fact, been part of a strategy to get ahead of damaging news stories.

Last May, Giuliani went on Sean Hannity's Fox News show and acknowledged that Trump repaid Cohen for hush money payments to Stormy Daniels, the porn star alleging an affair with Trump, a statement viewed then as a misstep but later perceived as an effort to minimize revelations about possible campaign finance violations.

After struggling to find a cable-ready defender, Trump has been mostly appreciative of Giuliani's attack-dog style - and, for a time, his broadsides against Mueller appeared to play a role in driving down the special counsel's poll ratings. But at other times the president has expressed dismay at Giuliani's scattershot style.

Part of his confusion is that while Giuliani frequently speaks to his client, the president's legal team has had a difficult time corralling Trump for a lengthy debriefing about the facts of the case, particularly from events stemming before the presidency, according to one official and a Republican close to the White House.

Still, Giuliani is regarded as an important member of the legal team. A former federal prosecutor, he has also been the team's public face and, even if not the primary author of letters and other documents to the Mueller team, he has nonetheless helped develop strategy.

TV networks have not shown any reluctance to book Giuliani, despite his unreliability, because of his rock-solid resume and the lack of other Trump surrogates willing to appear on a cable network other than the Fox News Channel.

'I am afraid it will be on my gravestone. "Rudy Giuliani: He lied for Trump." Somehow, I don't think that will be it,' Giuliani told The New Yorker. 'But, if it is, so what do I care? I'll be dead. I figure I can explain it to St. Peter.'

Press Secretary Sarah Huckabee Sanders did not respond to questions Tuesday about whether Trump still had confidence in Giuliani.