The US president’s Twitter feed has become an apparently inexhaustible source of dismay and disgust. Today it was a tweet from his namesake son that dropped jaws. Under pressure over his meeting with a Kremlin-connected lawyer, Donald Trump Jr released the relevant emails. They show that he was invited to meet a lawyer representing the Russian government to see information “that would incriminate Hillary [Clinton]”, as “part of Russia and its government’s support for Mr Trump”. The go-between added helpfully: “I can also send this info to your father.”

Mr Trump Jr responded enthusiastically – “If it’s what you say I love it” – and formatting suggests he forwarded the messages to Paul Manafort, then campaign chairman, and Jared Kushner, his brother-in-law. All three attended the meeting at Trump Tower. It took place after the Democratic National Committee had been hacked, but before material had been made public. Hours later, Mr Trump Sr tweeted at his rival: “Where are your 33,000 emails that you deleted?” Reince Priebus, the White House chief of staff, has dismissed the issue as “a big nothingburger”. There seems to be a lot of meat in the bun.

Mr Trump Jr stressed that the lawyer was not, in fact, a Russian government official. But he met her believing that she was, and having heard that Moscow wished to intervene in a US election. He did not report the approach to the FBI. The incompetence and dishonesty of the Trump administration has a bleakly comic edge. But let no one doubt the seriousness of these developments. Tim Kaine, Mrs Clinton’s running mate, warned that questions were moving beyond obstruction of justice, “into perjury, false statements, and even potentially treason”.

The clouds over the president’s head are gathering. Last week in Hamburg, he held his first meeting as leader with Vladimir Putin – a lengthy love-in. There was no sign of much progress on the pressing global issues – Syria, Ukraine and arms control included– so dearly in need of resolution. Instead, the Russian foreign minister has said that Mr Trump listened as Mr Putin told him that Moscow did not run a hacking and disinformation effort, and said “that he accepted these statements”. After all, the US president has repeatedly questioned his own intelligence agencies’ conclusion of Russian meddling. Today’s email release makes it both breathtaking and shocking that a US president can simultaneously accept Mr Putin’s denials and rage against the US press. But he and his entourage have the loosest relationship with the truth. Weeks after the meeting, Mr Trump Jr dismissed “disgusting” and “phoney” claims that Russia was helping his father’s campaign. Only this weekend he claimed the encounter was to discuss adoption issues.

Many are now asking if this email chain is the smoking gun. The question is who will employ this evidence. The special counsel Robert Mueller’s remit goes beyond the president’s personal role, to look at his campaign and at Russian intervention more generally; but his investigation is likely to take another year or so. Nor is it beyond possibility that Mr Trump might lever him out, like he sacked the FBI director James Comey.

The second course is impeachment. The political obstacles are substantial given the hefty Republican majority in both chambers. The party knows the president is both shameful and toxic. But with the midterms less than 18 months away, majority leader Mitch McConnell and speaker Paul Ryan are still standing by their man, putting political self-preservation above the interests of party or country. Many of Mr Trump’s grassroots supporters seem remarkably unmoved. His constant complaints of fake news have perhaps proved effective – clouding the picture enough to obscure the facts. Yet slowly and inexorably, he is being trapped between a disastrous self-interested flirtation with a ruthless Russian leader and the readiness of the American legal system and its free press to investigate the facts. In time, the haze will clear.