Boris Johnson limps on for now but for how much longer?

It was the blow to Boris Johnson that every one of his backbench critics had been waiting for.

Sajid Javid, the health secretary, followed shortly by Rishi Sunak, the chancellor, posted their letters of resignation on Twitter, criticising the competence of the government.

Related: Rishi Sunak and Sajid Javid’s resignation letters in full

Neither explicitly mentioned the sexual misconduct and Partygate scandals that have dogged the government for months. Sunak in particular claimed the prompt for his resignation was his differing approach on the economy.

But the backdrop to both resignations was Johnson’s catastrophic handling of the Chris Pincher affair, after he admitted appointing his ally as deputy chief whip despite having been told of misconduct allegations against him.

Just seconds earlier, Johnson had told the cameras that he was sorry for his mistakes in appointing Pincher, and he had toured the House of Commons tearoom saying that “everyone deserves a second chance”.

The problem is that Johnson is not on his second chance but a number much higher than that after scandals such as Partygate, Tory donors funding his flat renovations, his overriding of Security Service advice to give a peerage to Evgeny Lebedev, and attempts to rewrite the standards system.

The two major resignations did not lead to an immediate further deluge of cabinet ministers quitting but Tory MPs critical of Johnson still believe this means the end is nigh for the prime minister.

There are now two heavyweight opponents of the prime minister on the backbenches, where they may be able to devote more time to building leadership campaigns to eventually succeed him. Sunak and Javid will also – like Jeremy Hunt – be able to offer a critique of Johnsonism from outside the government. A string of Sunak supporters, including Huw Merriman and Kevin Hollinrake, were among those to applaud the former chancellor.

There is also a possibility of further government resignations trickling out over the coming days, giving a sense that Johnson is unable to command enough support to fill all the spaces in his government.

If that does not happen, the focus is on the 1922 Committee elections, which are likely to result in a slate of Johnson critics being elected and the rules being changed in favour of holding another confidence vote on the prime minister’s future.

Johnson has maintained the confidence of his party by a slim margin – but it would only take about 32 MPs to switch side at some point in the coming months for his premiership to be over.

Some remaining cabinet ministers loyal to Johnson have discussed battening down the hatches in the hope of Keir Starmer getting fined by Durham police within days, one cabinet source said.

They believe it may be possible for Johnson to ride out the storm if attention could soon be turned on to a leadership and ethics crisis in Labour.

But equally, the situation feels unsustainable to many Tory government aides. “I’m just detecting more despair,” one says. “Ministers and civil servants are behaving like there’s no one in control. Because No 10’s bandwidth is so consumed by this. You cannot get the system to work efficiently during this time. It’s just another shitshow. But I think it feels different in that patience is wearing thin.”

Another cabinet source said: “We limp on.”