Pete Hegseth, Donald Trump’s Secretary of War, made a jaw-dropping announcement this month: the US would livestream the execution of Nidal Hasan, the former US army major who killed 13 people and injured 32 more in a mass shooting at the Fort Hood military base in 2009.

Eight days later, after much public scrutiny, Trump made an announcement of his own: the livestream would not be happening after all, though Hasan’s execution by firing squad is still scheduled to go ahead on 3 December.

Hegseth, one of the most prominent faces of the Trump administration, had very publicly announced the public execution, the first in America in 90 years, the Pentagon’s announcement with a single word: “Justice.”

He told right-wing cable channel Real America’s Voice that he had ordered the public execution, while calling the firing squad a “no-brainer” and framing it as reciprocal justice that would mirror Hasan’s crimes.

Now he looks out of sync with his boss, which is never a good place to be in Trump’s White House. (Trump showed initial enthusiasm for the plan but appeared to distance himself after the public backlash.)

Hegseth is rarely camera-shy, but so far at least he hasn’t issued his own statement or been seen in front of camera since Trump’s announcement, where he said that “many very good and well-meaning people would rather not watch him die”.

One thing that can be said for Hegseth’s plan is that it united a nation that is so often divided, albeit uniting it in opposition to his plan. Polling by Ipsos showed that 80 per cent of Americans – including 64 per cent of Republican voters – thought the execution should not be streamed, versus just 18 per cent of adults who were in favour.

The proposal also attracted an unusual level of backlash even from senior Republicans, who usually avoid publicly criticising their own party just weeks before an election. It seems that sometimes an idea is just so obviously bad that it can cross party lines, even in Trump’s America.

Hasan’s 2009 attack was motivated by radical Islamist ideology, which often aims to portray Islam and Western democracy as incompatible, with a goal of escalating conflicts between the two. Few Islamist attackers are concerned with protecting their own life. Hasan probably expected to die during his attack, which only stopped when he was shot. He survived, but was paralysed from the waist down.

Critics pointed out that the public execution of a man in a wheelchair, who used violence for propagandistic ends, would almost certainly backfire. Others noted that mass shooters often commit their crimes in the hope of gaining notoriety – a public execution would definitely offer that.

Hegseth’s plan, in other words, might have been offering potential killers exactly what they sought.

Meanwhile, no one in Hegseth’s orbit seemed to have thought through the possible consequences of his announcement. Al-Qaeda and other Islamist groups around the world have suggested that they would publicly execute hostages if the livestreamed execution went ahead.

Hegseth, a defence chief who often seems out of his depth tackling even simple issues, had walked the Trump administration into a nightmare position – announcing a move unpopular with his own party, hated by the general public and likely to lead to reprisals. All, seemingly, for no reason other than he appeared to think a livestreamed execution would be somehow cool and macho.

But then again, Hegseth also doesn’t seem to have thought through the basics of how a livestreamed execution would even work. Would it air on YouTube? Facebook? Both social networks have strict rules banning such content. Did he expect US television networks to air the execution? Would he try to force networks to air the execution if they came out against doing so?

It was a mess, and one that was increasingly distracting the Trump administration in the lead up to midterm elections that polls predict will be a disaster for Trump and his Republican colleagues.

On one level, this is hardly the biggest mistake Hegseth has made. He was widely reported to have been an early cheerleader for the war with Iran, but when it didn’t work out according to the most optimistic assessments – the idea the regime would collapse within weeks if not days – he has tried to talk about almost anything else.

But if neither Hegseth nor Trump know how to end that war, they are, at least, in the same boat. With his livestreamed execution debacle, Hegseth has created a self-contained crisis of his own making.

Trump has proven time and again that there is no one so close to him that he won’t fire them. This week, he sacked Kimberly Guilfoyle as US ambassador to Greece after controversies over her reportedly asking a Republican donor to pay off a $100,000 (£75,390) credit card bill. (Guilfoyle was once engaged to Trump’s eldest son.)

Guilfoyle’s lawyers denied that she had done anything wrong, and said the money she was seeking was payment for public appearances and speaking engagements.

At a time when Trump may be looking for more scapegoats after the midterms, or people to cut adrift to revamp his team, Hegseth has almost volunteered himself to be considered for a clear out.

Proposing a livestreamed execution might not be the worst mistake Hegseth has made as Trump’s Secretary of War – but it could prove to be one of his last.