Indeed, hours before Gaetz stood down, Fox News presenter Peter Hegseth, who Trump has tapped to run the Pentagon, was accused in a newly released police report of raping a woman who claims he took her phone, blocked the door of his hotel room and refused to let her leave.

Hegseth, a 44-year-old army veteran with no government experience, was never charged over the incident, which took place when he was a keynote speaker at a California Federation of Republican Women conference in October 2017.

But the graphic report released by police overnight offers the first detailed account of what the woman alleged transpired – and one that is at odds with Hegseth’s version of the incident, which he insists was consensual.

As Hegseth’s nomination came under growing concern, a lawsuit also resurfaced against World Wrestling Entertainment co-founder Linda McMahon, who Trump has picked to be his new secretary of the Education Department.

It alleges McMahon knowingly enabled the sexual exploitation of children by a WWE employee as early as the 1980s when she ran the global conglomerate with her husband, former chief executive Vince McMahon.

According to the lawsuit, filed last month on behalf of five men who were 13 to 15 at the time, the now-deceased employee was a paedophile who recruited kids to work as “ring boys” – who would assemble and disassemble wrestling rings – as a guise to exploit and sexually abuse them.

McMahon, a long-time ally of Trump who served as his transition co-chair and the former head of the Small Business Administration, rejects the claims that she was negligent, describing the allegations through her lawyer as “scurrilous lies, exaggerations and misrepresentations”.

Whatever the case, all eyes will soon turn to the new Senate, where a nominee needs a simple majority from the chamber’s 100 senators to be appointed. Republicans hold 53 seats to the Democrats’ 47, meaning a few defections could torpedo Trump’s picks.

Will enough of them push back on Hegseth, as they did with Gaetz, or downgrade McMahon in any way?

Loading

What will they make of Robert F. Kennedy Jr, the vaccine conspiracy theorist who Trump has tapped to run the Department of Health and Human Services? Or celebrity doctor Mehmet Oz, who has promoted unproven COVID-19 treatments and has now been nominated to lead the Centres for Medicare and Medicaid Services?

What about former Democrat congresswoman Tulsi Gabbard, who is seen as such a Russian sympathiser in some quarters that a Kremlin-controlled news show recently referred to her as “our girlfriend” as they hailed her nomination as Trump’s director of national intelligence?

If appointed, Gabbard’s job as director would be to supervise and co-ordinate the work of all 18 US intelligence agencies. But Republicans on the Senate Intelligence Committee have already indicated they will probe her past actions – which include a controversial meeting with Syrian dictator Bashar al-Assad, a key ally of Russian President Vladimir Putin, during a trip to the country where she dismissed his US-backed opposition as “terrorists”.

Several Democrats have also made it clear she will not have their support, and have questioned whether America’s “Five Eyes” partners – Australia, Canada, New Zealand and Britain – would be equally concerned.

“I do not think that she’s someone who can be trusted with the nation’s secrets, and I do not think our Five Eyes allies, or our allies around the world, will trust her with theirs,” said Florida congresswoman Deborah Wasserman Schultz.

“It’s like the Star Wars Cantina of cabinets, and it’s really going to jeopardise America’s safety.”

Trump has wasted no time tapping loyalists to help him carry out his second term agenda. But as Gaetz’s demise has shown, there are no guarantees of getting them approved.

Get a note directly from our foreign correspondents on what’s making headlines around the world. Sign up for our weekly What in the World newsletter.