Winter is here, the Tories are out of control and Sunak is running out of options

Rishi Sunak can govern the country or manage the Conservative party, but not both. He will probably accomplish neither, for the same reason that it is impossible to move in different directions at once while also standing still.

It is impossible, for example, to build houses and not build them, although that is now the government’s plan. Sunak has yielded to Tory rebels who oppose an annual target of creating 300,000 new homes. Last week the levelling up and regeneration bill was pulled from the Commons when enough MPs backed an amendment scrapping the target. The prime minister has agreed that the number will be merely “advisory”, and that local authorities can discount it if constructions threaten to change the character of an area.

Since many local people and their MPs measure such character by the absence of new-build houses, the target is dead. So is any notion that the government intends to grapple with the housing crisis or prioritise the interests of those who are desperate to own their own homes over those who have one already.

That is a rational choice for Conservatives whose majorities are sustained by comfortably housed older voters. For MPs who need to recruit supporters under the age of 40, the incentives go the other way.

It is common enough for a government’s national agenda to rub against some party interests on the ground. That is where leadership comes in. Downing Street is supposed to whip recalcitrant underlings into line using the familiar arsenal of persuasion and coercion – appeals to the benefits of a united front and the perils of aiding the opposition; offers of promotion, some other favour or the threat of favour withdrawn.

But Sunak has no ammunition. The Tories are unwhippable. After 12 years in government, the backbenches are cluttered with ex-ministers, their forsaken ambitions and their accumulated grudges. Traffic in and out of the cabinet has been especially busy this year, with two regime changes. That double defenestration means pretty much every Tory MP has rebelled against one leader or another at some point. Insurrection is embedded in the culture of the party.

Those misaligned egos could be made orderly by the prospect of election victory, but that looks remote. It is hard to picture Sunak as a winner when he reached Downing Street by way of defeat and default: losing to Liz Truss over the summer, crowned by acclamation in the autumn when his rivals stood down. At least 100 MPs thought it was a better idea to bring Boris Johnson back. Their allegiance is coloured by a view of Sunak as his former patron’s assassin. Friends of Caesar are not loyal to Brutus.

Opinion polls show Sunak is more popular than his party, which suggests that his MPs’ electoral prospects would be enhanced by submission to their leader. Instead, they are forming a vicious circle. Rebellion weakens the prime minister, whose debilitation encourages more demands for policy concessions, to the point where Downing Street has no agenda distinct from survival through the latest crisis, and deferral of the next one.

It is an ailment more familiar in prime ministers without large Commons majorities, and who have been in power for more than two months. Sunak has achieved stasis at speed – an unusual combination. He is also notably inconspicuous for a man with the bully pulpit at his disposal. Attention is one resource a prime minister can command at will and in abundance. There is enough heft in the office that its weakest incumbents can influence the terms of debate by simply turning up. They can invade the news agenda with a press conference or speech. But first they need something to say.

Sunak’s voice doesn’t carry. At first, around the time of the autumn statement, the political agenda was clearly dictated from Downing Street. But that was a function of the set-piece occasion. Westminster clears its diary, and newspapers reserve their front pages for a budget. Since then, Sunak’s time has mostly been spent defending, rejecting, reacting.

He has lost one minister to allegations of bullying while another is under investigation for the same alleged offence. He has been forced to reassure Brexit hardliners that he shares their abhorrence of a “Swiss-style” reintegration with the EU. He has said that stricter control of cross-Channel migration is his “most pressing priority”, which is probably true as diagnosis of a persistent electoral headache in need of treatment but not as an account of his motives for wanting to be prime minister in the first place. Those remain obscure, although he has not lacked opportunities to spell them out.

It doesn’t help that his legislative programme is inherited from discredited predecessors. The levelling up bill is just the first chapter in an anthology of parliamentary pain. There are two Brexit bills in the pipeline. One repudiates the Northern Ireland protocol, thereby flouting international law and undermining any hope of a diplomatic rapprochement with Brussels. The other would erase the legacy of European regulation from the statute book with indiscriminate zeal. That process is abhorred by the very businesses for whose sake the bonfire of red tape is supposed to be lit.

Sunak knows both bills need dilution, and also that amendments will be denounced as heresies by Eurosceptic puritans in parliament. That is a battle he could do without as Britain drifts into a grim winter, where people will be concerned mostly by the struggle to make ends meet, and by the parlous state of public services. As time goes on, the needs of the country and the fixations of Conservative MPs will diverge faster and harder. The prime minister wants to satisfy both. It can’t be done. He will be torn apart if he tries.

• Rafael Behr is a Guardian columnist