There is a scene in Shattered, Jonathan Allen and Amie Parnes's book about Hillary Clinton's presidential campaign, that describes the feeling inside the Clinton camp when a recording of Donald Trump boasting about assaulting women surfaced just a month before the election.

The bombshell Access Hollywood tape, on which Trump said he liked to grab women "by the pussy", reverberated across the world and prompted several senior Republicans to publicly criticise their presidential nominee. There was serious talk in Republican circles about replacing Trump on the ballot. News channels wondered if his campaign was over. But then a poll was released. It showed that only 13 per cent of Republicans said they were less likely to vote for Trump because of the video, which had been recorded in 2005. The book recounts the "terrifying realisation" in the Clinton camp that the controversy was not going to affect Trump's electoral chances in 2016.

The man who once boasted that he could stand in the middle of Fifth Avenue “and shoot somebody” and not lose votes looked set to ride out the storm.

This week brought another of those moments.

Say that again? US intelligence chief surprised by news of Putin visit

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Putin warns of Ukraine ‘escalation’ as mystery shrouds Trump talks

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Trump renews attack on ‘fake news media’ coverage of Putin summit

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Trump's press conference with Vladimir Putin, his Russian counterpart, at their summit in Helsinki was widely seen as one of the most misguided and potentially damaging moments of a chaotic presidency. Coming directly after a turbulent trip through Europe, during which he disparaged the leadership of Theresa May and Angela Merkel and repudiated his Nato allies, Trump arrived in Finland for his first one-to-one meeting with the Russian leader. As the world looked on incredulously, the president of the United States refused to condemn Russia for election interference, said that "both sides" were to blame for deteriorating Russo-American relations and rambled about Clinton's email server and the "fake news media".

After a brief but deafening silence from the Republican establishment, criticism flooded in from conservative commentators and lawmakers. The verdict was virtually unanimous: Trump had dangerously misfired. The veteran Republican senator John McCain said it was "one of the most disgraceful performances by an American president in memory" and lambasted Trump's "naiveté, egotism, false equivalence, and sympathy for autocrats".

The chairman of the United States Senate's foreign-relations committee, Bob Corker, said the president had "made us look like a pushover".

But the criticism also came from close Trump allies. Newt Gingrich, a long-time supporter, said it was the "the most serious mistake of his presidency" and needed to be corrected.

By Tuesday the White House was trying to limit the damage. The president claimed to have mis-spoken during the press conference: he meant to say "wouldn't" instead of "would" when he said he saw no reason why Russia would meddle in the election.

Further mixed messages emerged over the following days. Trump was forced to clarify that he opposed a Russian proposal to allow Moscow to question 11 former US officials and diplomats; he had previously welcomed it as an "interesting idea" – a comment that prompted an alarmed Senate to hold an emergency vote.

But by Thursday the president was back into full defensive mode, lashing out at the "fake news media" as the enemy of the people, with the White House announcing that he had instructed his national-security adviser, John Bolton, to invite Putin to Washington in the autumn. As the fallout gripped the country, questions remained about what went on between the two men during their two-hour private meeting, prompting calls from Democrats for the translator who had been its only other attendee to be subpoenaed. Suggestions from Russia that the two men had reached agreements on certain issues sparked alarm at the US state department and at the Pentagon.

The public break between Trump and senior members of the Republican establishment has again raised one of the central questions of Trump’s presidency: how far is his party prepared to back him?

Although congressional Republicans grappled in the early months of the Trump administration with a leader whom many had opposed as a candidate, the Republican establishment generally rowed in behind him as his presidency bedded down. With Trump benefiting from a particularly strong few months in the polls – his summit with Kim Jong-un has played well with the public – most have refrained from criticism.

But could things be about to change?

This week has seen a host of Republican insiders lambast Trump, from the former governor of New Jersey Christine Todd Whitman to the long-time strategist Steve Schmidt. Last month Schmidt, a former aide to McCain and George W Bush, renounced his membership of the Republican Party after 30 years because it had become "fully the party of Trump".

In particular, Trump has misfired spectacularly on an issue close to Republicans’ hearts: foreign policy. Trump’s justification for meeting Putin – that it is a “good thing”, not a “bad thing”, that the US is talking to Russia – has mortified many Republicans, who are astounded that their president failed to confront the man whom US intelligence agencies have said directly ordered the intrusion into the United States presidential election. The image of Trump as appeaser-in-chief is alarming many in the party.

But although this week was undoubtedly a low point for his presidency it is unclear whether it will be a turning point. CBS found this week that only 21 per cent of Republicans disapproved of Trump’s handling of the Helsinki summit while 68 per cent of Republicans approved.

This early indication that Trump's base is holding may explain the president's confidence on Twitter by the end of the week, when he boasted about the success of the summit and lashed out at the "fake news media" for its coverage of the meeting.

Similarly, away from the Washington bubble, Republican Party members, particularly those contesting this year's midterm elections, are likely to be wary of opposing Trump, given the strength of his core support. Trump remains a powerful ally for many Republicans hoping for success in November's ballots, particularly for those contesting primaries in heavily Republican states. This week we got a taste of Trump's readiness to wade into local electoral politics. Amid all the Putin controversy this week he still found time to tweet his support for Brian Kemp, a hard-line Republican hoping to become governor of Georgia, who shares many of Trump's anti-immigration views. Kemp is hoping that Trump's public endorsement of him – "Brian is tough on crime, strong on the border and illegal immigration" Trump tweeted on Wednesday – will help him defeat his rival for the nomination, Casey Cagle, in a run-off next week.

As the dust settles on the Helsinki fiasco, two things may determine the summit's effect on Trump's legacy. The outcome of Robert Mueller's investigation into Russian interference continues to loom over events, with Republicans privately wondering if the special counsel does indeed have seriously incriminating information about the president, as they try to explain Trump's extraordinary reluctance to criticise Putin. Secondly, any rumblings from North Korea in the coming weeks or months could spell trouble for Trump. Pyongyang's lack of progress in denuclearising has largely gone unnoticed by the US media; if North Korea acts aggressively or repudiates the terms of the Singapore summit it could seriously damage the American president's standing and foreign-policy credibility.

Trump's base may like the rabble-rousing, anti-immigrant nationalism that the president continues to espouse. But any suggestion that he could become a modern Neville Chamberlain – the British leader infamously declared "peace in our time" after meeting Hitler in Munich in 1938 – will not go down well. Trump's decision to sit down with two of the world's most authoritarian leaders yet return to Washington with nothing substantive in return may turn out to be the biggest gamble of his presidency.