For a moment after the January 6 invasion of Capitol Hill, it looked like a critical mass of Republicans might sever their ties to Donald Trump. His thinly-attended farewell this week seemed to encapsulate his plunge in fortune.

A lot of this was wishful thinking. Several hours after the assault on Congress, two-thirds of Republican representatives voted against certification of Joe Biden’s victory. A week later, just 10 Republicans voted to impeach Mr Trump, barely 5 per cent of the party’s House of Representatives caucus.

The rebels are already paying a price for their disloyalty. Liz Cheney, the most prominent among them, is being challenged for her leadership position — she is the Republican chief whip. Ms Cheney also faces a primary challenge for disloyalty to Mr Trump. The same applies to most of the other nine. With more than $200m in campaign funds, Mr Trump has made it clear he will try to punish the heretics from the safety of Mar-a-Lago. He is by no means planning to fade into the Florida sunset.

The question is not whether the Republican party can turn over a new leaf; that is off the cards in the near future. It is how Mr Biden’s Democrats should handle an opposition that is vowing to obstruct most of his agenda. Mr Biden faces a dilemma. In his inaugural address on Wednesday, he promised to foster a climate of unity and healing. Yet he also vowed to “reject a culture in which the facts themselves are manipulated, even manufactured”. Since much of the Republican party remains yoked to conspiracy theory — including the ultimate lie that Mr Biden stole the 2020 election — it is hard to see how he can meet them halfway.

Next week’s Senate trial of Mr Trump will give some pointers. Mitch McConnell, the Senate Republican leader, this week said the former president had provoked the mob that ransacked Congress. This came close to the wording of the article of impeachment, which charges Mr Trump with “incitement of insurrection”. But no Republican senator, including Mr McConnell, has yet said they will vote to convict him. It would require 17 Republicans for the necessary two-thirds majority.

This time last year in Mr Trump’s first impeachment trial, only Mitt Romney voted to convict — for abuse of power. By contrast, a growing number of Republican senators say they will reject the trial as unconstitutional since it will take place after Mr Trump has left office. Among the handful who might be more sympathetic to convicting Mr Trump, such as Alaska’s Lisa Murkowski and Ohio’s Rob Portman, the threat of primary challenges loom. Both senators face re-election in 2022.

The energy in the party is clearly with those vying to inherit Mr Trump’s mantle, notably Ted Cruz of Texas and Missouri’s Josh Hawley. The newest stars in the House include two promoters of QAnon, the pro-Trump conspiracy theory: Marjorie Taylor Greene of Georgia and Lauren Boebert of Colorado. In a healthier democracy, the Republican party would be debating where it went wrong, having lost the White House and the Senate. Instead it is embracing the language of betrayal.

There is still a chance for the party to stick with some sounder elements of Trumpism — such as helping the left-behinds of globalisation — while rejecting eccentric, self-serving leadership that peddles anti-democratic myths. The US desperately needs a principled conservative party that stands up for the constitution and the free market.

Mr Biden should still keep his bipartisan hand outstretched. Should it be spurned, he must level with the US people. Healing is only possible when all parties agree to the basic rules of democracy.