Is Theresa May heading for disaster? It's very difficult to escape that conclusion this evening. Her plan for a soft Brexit continues to lose her friends and alienate people on the Tory benches.

Today Robert Courts, David Cameron's successor as MP for Witney, became the sixth member of the government to quit since the cabinet signed off on the Chequers proposal.

His resignation, as with that of Chris Green last week, is one of those likely to elicit a one-word reply from most observers: "Who?" In the immediate term, May will obviously survive without a parliamentary private secretary to the junior ministers at the Foreign Office, as she has without Boris Johnson and David Davis.

It nonetheless spells trouble for the prime minister ahead of key votes on the Trade and Customs Bills this week. Last month, it appeared that the greatest risk for the government was rebellion from pro-EU Tories. Instead, the Brexiteers now pose a clear and present danger. Resignations like Courts' – not pathological rebels, but conscientious, upwardly mobile members of the government machine – highlight how pervasive the discontent with May's plan for Brexit is, and how far beyond the usual Eurosceptic suspects it extends.

Their unstoppable force is about to meet an immovable object. The prime minister made clear on Marr and in today's Mail On Sunday that she is not for turning – warning rebels that it is her Brexit, or no Brexit.

Her problem – and it is getting bigger by the day – is that nothing will convince them to support the Chequers plan. Indeed, Steve Baker, the former European Research Group chair who resigned as a Dexeu minister last week, is now running a "party-within-a-party" whipping operation to corral Eurosceptic colleagues into opposing it (as revealed by the Telegraph).

I wrote last week that Baker's resignation, rather than those of Davis or Johnson, had the most potential to destabilise May. So indeed it has. He is back doing what he does best – fomenting backbench rebellion. Baker and his ERG colleagues are clear they will not stop until May blinks, even if that means rebelling en masse on this week's legislation. They no longer trust the prime minister. "She is a Remainer who has remained a Remainer," Jacob Rees-Mogg complained today.

If May does not fold and resile from the Chequers plan – and there is no indication that she will – then the rebels' mission will shift to changing leader, rather than changing policy. "I'm afraid things are now on the verge of going properly pear-shaped for people's summer holidays," a source close to Rees-Mogg warned this afternoon.

With just one week left before parliament breaks for recess, and more resignations likely to come, an explosive showdown is inevitable. If both sides keep to the irecconcilable positions they currently occupy, it will mean a leadership challenge.