When Donald Trump famously descended the escalator of Trump Tower to announce he was running for president in June 2015, I found my thoughts immediately turning to Rudy Giuliani. Here was another son of New York City making a wildly unrealistic bid for the White House, just as Giuliani had done eight years previously. The former mayor reluctantly quit the field after months of trudging around Iowa and New Hampshire without winning a single delegate.

When Trump won, it seemed like a big reward was on its way to Giuliani. Would he be the next secretary of state, the pundit class speculated, after concluding that the role of attorney general wasn’t good enough for the former lawyer? Instead, word came from the White House that Giuliani had taken himself out of consideration, a statement no one believed. Giuliani turned out to be the next cyber-security tsar.

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So it was rather shocking when in April the announcement came that Giuliani was joining the Trump legal team and becoming its chief spokesman. Giuliani had been given perhaps the most important job of all: fighting Trump’s corner as Robert Mueller’s FBI investigation into Russian interference in the 2016 presidential election homed in relentlessly on the White House. During just over one and a half years in office, the president has lost or fired a succession of key administration figures, from Steve Bannon to Michael Flynn. Trust Trump to pick a top legal gun who creates more problems for him than he solves, which is what Giuliani seems to be doing.

In television interviews last week, Giuliani first revealed and then tried to kill a story that reporters were working on at the New York Times, involving allegations by the president’s former fixer Michael Cohen, whom he described as “an instinctual liar”. The story, according to Giuliani, alleged there was a strategic “pre-meeting” between senior Trump aides, before the now infamous Trump Tower encounter in 2016 between members of the then-candidate’s team and the Russian lawyer, Natalia Veselnitskaya, who was offering damaging information about Hillary Clinton. In rapid-fire sentences, some of which were barely comprehensible, Giuliani maintained that this pre-meeting never happened. So why did he bring up the allegation, which had apparently been put to White House officials, at all, deepening the intrigue surrounding the Trump Tower meeting? The same goes for another piece of hot information Giuliani dropped in May – that Trump had reimbursed Cohen for money used to pay off the stripper, Stormy Daniels, to stop her going public over an alleged affair with Trump. That placed his client more squarely in the frame of another matter under investigation by Mueller.

Facebook Twitter Pinterest New York governor George Pataki, Rudy Giuliani and Hillary Clinton tour the World Trade Centre site after the 9/11 attacks. Photograph: Robert F. Bukaty/AFP/Getty Images

These blunders are surprising because Giuliani is no rookie. He is a former US prosecutor known for jailing Wall Street titans and New York politicos, some of whom were pals of Trump. But watching his incoherent bumbling as Trump’s new lawyer, no one would suspect his distinguished legal past. His off-the-cuff delivery made it look like he was answering questions before even thinking them through, nor the possible ramifications of his answers. It was distinctly un-lawyerly. I’ve talked to influential business people in New York who know both men and did business with them in the 1990s, when Giuliani was New York mayor and Trump was rising as the city’s most egotistical developer. They say they no longer recognise the two men as the sharp, savvy acts they were back then.

It’s sad to witness this final, inglorious phase of Giuliani’s career, given the admirable parts of the first act. As mayor, he won the hearts of the world after 9/11, walking alongside the hero firefighters and those charged with rebuilding downtown. He used his legal chops to crack down on crime and to enforce order in a city that had spun out of control, although his sanctioning of police violence brought justified condemnation. Voters liked the fact that they could go outside without seeing or smelling piles of uncollected garbage. He became popular for making the city work again.

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But it increasingly seems like Trump has hired a liability. The wild, aggressive language should not be a surprise. Some of Giuliani’s campaigning for Trump bordered on the unhinged. Remember the first night of the GOP convention in Cleveland, Ohio, a speech notable for its “lock her up” histrionics? Then came Giuliani’s crazed-sounding defence of Trump’s outrageous comments about Muslims and cheap attacks on the press. The tone, especially for the convention’s opening, was angry and dark. But it is the apparent lack of legal smarts that should be alarming Trump. Giuliani seems totally outmatched by Mueller. Charges involving obstruction of justice and collusion with an enemy state, Russia, may be looming. The special prosecutor’s office is now trying its first case against Paul Manafort, Trump’s former campaign manager, who is on trial in Virginia for tax offences related to his lobbying in Ukraine.

Other former Trump advisers, such as Flynn and George Papadopoulos, have taken pleas, as has Manafort’s aide-de-camp, Rick Gates. More than a dozen Russians have been indicted for the 2016 election high jinks. There’s no telling what Mueller has.

Trump’s strategy has been to attack Mueller relentlessly. He wanted an attack dog to bite back at Mueller and there was no one more snarling than Giuliani. But he keeps messing up. On other talk shows last week, Giuliani denied Trump was guilty of any collusion. The next day he was arguing that collusion was not a crime, anyway. Which is it?

F Scott Fitzgerald famously wrote: “There are no second acts in American lives.” It might have been a blessing for Rudy Giuliani if that were really true.

• Jill Abramson is a Guardian columnist