“Rudy is in so many ways a perfect messenger for exactly what this administration stands for, and that's why voters reject it,” Biden deputy campaign manager Kate Bedingfield said, underscoring the campaign’s eagerness to use Giuliani as a White House poster boy.

Bedingfield also delighted in Trump’s attempt to distance himself from Lev Parnas and Igor Fruman after their indictments — a problem because the president and his son and namesake had been separately photographed with the two Soviet-born Florida businessmen. Before they were arrested Wednesday night at Dulles International Airport, the men were had planned to meet Giuliani in Vienna, Austria.

“Giuliani's cronies — who Trump pretends not to know even though he’s pictured with them multiple times giving the thumbs up, no less — have been arrested trying to flee the country, one day before Rudy was scheduled to join them in Vienna and hours after dining with him at the Trump Hotel,” Bedingfield noted.

Polls show Giuliani is deeply unpopular and likely a liability for Trump when it comes to public opinion — a fact noted by both Biden advisers and members of Trump’s inner circle, one of whom described the indictments and Giuliani’s previous and widely panned performances on cable news as a “disaster.”

Only 31 percent of voters have a favorable impression of Giuliani, while 53 percent view him unfavorably, giving the former mayor a negative net favorability rating of -22 percent, according to a Fox News poll released this week but taken before the indictments of his associates. Trump’s net favorability rating is also negative, -13 percent, while Biden’s is positive at 6 percent in the poll.

Underpinning Giuliani’s poor standing with voters: a relatively high number of Republicans view him unfavorably (29 percent) while independents give him a net rating of -41 percent and Democrats of -58 percent. Giuliani only polls better with Democrats when compared with Trump in the Fox poll.

“The president would be better served if Rudy wasn’t on television,” said a top Trump adviser, echoing three other similar sources. “The president would be better off if Rudy was not the face of this. No one really likes him, but somehow we’re stuck with him.”

Giuliani did not return calls and messages for comment.

A former Giuliani adviser, Rick Wilson, said the former mayor and federal prosecutor “lost his way” as he became a lobbyist and insider. He had his own deals overseas and got so entangled in them, Wilson said, that he was like Trump’s now-convicted former campaign manager, Paul Manafort, who had so many interests in Russia and Ukraine that “he became like an Eastern European warlord.”

Giuliani, Wilson said, was transmogrifying into an object of ridicule akin to a "Looney Tunes" character known for schemes that always fail and backfire.

“Rudy has become the Wile E. Coyote of this scandal,” said Wilson, who advised Giuliani when he was New York mayor in the 1990s and early 2000s, a potential U.S. Senate candidate in 2000 and a presidential candidate in 2008.

“Rudy’s out there running off of cliffs, smacking into road signs and watching his own schemes just blow up on him to defend Trump,” Wilson said. “And if defending Trump is like catching the Road Runner, Giuliani is going to do that everyday and fail, no matter how absurd the situation is that he finds himself in.”

The animus between Biden and Giuliani traces back decades, famously surfacing in their respective failed bids for the presidency in 2008, after which Biden joined Barack Obama’s successful ticket and served as vice president until 2017.

At the time they were running, Biden accused Giuliani, who had earned such high marks for managing New York City after 9/11 that he was nicknamed “America’s mayor,” of cynically using the tragedy for political gain years later.

“There's only three things he [needs] to make ... a sentence: a noun and a verb and 9/11,” Biden joked , calling Giuliani “probably the most underqualified man since George Bush to seek the presidency.”

Giuliani biographer Andrew Kirtzman said the 9/11 gibe would have stung the former New York mayor.

"His 9/11 halo was everything to Giuliani — his experience that day changed him and became intrinsic to who he was. He had to have been deeply angered by what Biden said," Kirtzman said.

Earlier this year, Giuliani fired back at Biden over the 1994 crime bill that has become something of a political liability for the Democrat in the primary. Both Biden and Giuliani had worked for its passage.

“The 1994 Crime Bill passed by Pres. Clinton and Speaker Gingrich, with Biden & Schumer as the leaders in Senate and House, helped me and the NYPD reduce murder from @ 1,900 a year to @ 500 and then under Mayor Bloomberg to @ 350. That’s over 20,000 lives saved,” Giuliani tweeted May 15, before Trump’s latest attacks on the law.

Referring to pressure on Biden to disavow the bill, Giuliani added: “Joe don’t cave.”

Biden isn’t the only Democratic presidential candidate to zero in on Giuliani: Minnesota Sen. Amy Klobuchar called on Attorney General William Barr and the Federal Election Commission to investigate Giuliani for potential campaign finance violations.

More than a year after Trump took office — and after the president’s personal attorney Michael Cohen was convicted in a separate federal campaign finance scheme involving hush-money payoffs to a porn actress — Giuliani began working as Trump’s personal lawyer in Ukraine.

Since then, Giuliani has been the prime force driving Trump to focus on attacking Biden’s son Hunter Biden over a lucrative consulting contract for a Ukrainian natural gas company, Burisma, when his father served as vice president.

A Ukrainian prosecutor, Viktor Shokin, had been investigating Burisma, and Joe Biden successfully pushed for his ouster; Giuliani and Trump have characterized the situation as a quid pro quo.

But the prosecutor’s investigation into Burisma had stalled long before, numerous Ukrainian officials say, and Shokin’s ouster was due to standing U.S. policy and international pressure to get rid of him because of perceptions he was corrupt and ineffective.

In TV appearances, Giuliani has waved around an affidavit signed by the disgraced former prosecutor who swears he was dismissed because of the Burisma investigation. Unmentioned by Giuliani: the affidavit is filed on behalf of a Ukrainian gas magnate, Dmitry Firtash, who is employing two Trump loyalist attorneys to fight extradition to the U.S. in another corruption scheme.

An ally of Russian President Vladimir Putin, Firtash lives in Vienna, Austria, where Giuliani’s now-indicted associates, Parnas and Fruman, were headed on one-way tickets.

Both Giuliani and Trump have pressed Ukrainian officials behind the scenes to open an investigation into the Bidens. During a phone call with Ukraine’s president in July, Trump asked for an investigation into Biden as the United States withheld financial aid — a move that led to the impeachment inquiry in the House.

At first, Giuliani denied on television that he ever pressed Ukraine to investigate the Bidens. But he reversed himself in the same Sept. 19 interview with CNN’s Chris Cuomo, admitting that, yes, he did push for the investigation.

The Biden campaign reacted to Giuliani’s double-talk by calling on cable news to ban him, asserting that he’s a fount of disinformation.

At the same time Giuliani had been trying to gin up an investigation of Hunter Biden and the natural gas company he worked for, a group of businessmen and GOP donors name-dropping Giuliani and Trump were reportedly working in Ukraine to get a piece of lucrative natural gas contracts steered to Trump allies. Giuliani’s entanglements have become so suspect that conservative columnists have also fretted that he’s “taking Trump for a ride.”

On Wednesday, when Biden first called clearly for Trump’s impeachment, the candidate singled out Giuliani, mocking his ethics.

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“Now there are reports that not only did Trump send Rudy Giuliani, his personal lawyer, to carry out his scheme and co-opt the State Department — and, as alleged, allies of Giuliani were also working a side deal at the same time to make millions in Ukraine,” Biden said. “A corrupt scheme with an additional helping of corruption and self-dealing on the side: Classic Trump. The abuse of power is the defining characteristic of the Trump presidency.”

On Friday, Giuliani’s name was brought up again, this time with House impeachment managers, who took testimony from U.S. diplomat Marie Yovanovitch. She had been ousted from her job in Ukraine after Giuliani became a point man in spreading unfounded smears in right-wing media against her.

“I do not know Mr. Giuliani's motives for attacking me,” she said in a written statement. “But individuals who have been named in the press as contacts of Mr. Giuliani may well have believed that their personal financial ambitions were stymied by our anti-corruption policy in Ukraine."

Meanwhile, other Republicans, such as Florida Gov. Ron DeSantis, ducked for cover and had to return what they believed had been tainted political contributions from Parnas and Fruman.

Biden’s campaign reacted with a fundraising pitch to donors.

“The tide is turning,” the campaign wrote. “These Trump allies who helped Rudy Giuliani try to smear Joe Biden in Ukraine will face a court of law and the Trump Administration is facing an impeachment inquiry.”

Sally Goldenberg contributed to this report.