Could a general election be looming? It might seem unlikely. Last time Theresa May dissolved parliament, she had a 24-point lead and higher personal ratings than Margaret Thatcher or Tony Blair in their pomp. Labour had suffered one of its worst postwar defeats just two years earlier. And yet the Conservatives lost their majority. This time round, Labour are ahead in several polls. Jeremy Corbyn’s team, though tired after their journey from the political wilderness to the epicentre of the greatest political upheaval since the war, will begin an election with far more experience than last time. As senior Conservative officials have pointed out to the Sun, 40 Tory seats are held by a margin of less than 5%, with Labour in second place in 35 of them. How would voters view the fourth national vote in five years (the fifth for Scottish voters)? Brenda from Bristol would be considerably more irate this time. Would Tory MPs really let May take their party into an election, just weeks after 117 of them voted against her leadership? Are they not uniquely fearful of a Corbyn government, which they rightly judge to be a totally different prospect to a “normal” Labour administration?

And yet. May’s Brexit deal has suffered the biggest defeat in the history of British democracy. If she halved the margin of defeat in another vote, it would still find a place in the five worst parliamentary routs. How on earth is she supposed to turn a 230-vote deficit into a victory of at least one, in a matter of weeks? She won’t get a meaningful concession on the backstop from the EU: how will she get the DUP, all the hard Brexiteers of the Tory ERG and Tory remainers on side? Jacob Rees-Mogg is showing signs of surrender to May, but a hardcore would not follow him. If she is expecting mass Labour defections to back her deal, disappointment beckons. May is in an impossible situation of her own making.

What of the other options? Even if the Labour leadership instructed its MPs to back a second referendum – which would immediately trigger mass resignations from its frontbench – many in leave seats would refuse to do so, as would the vast majority of Tory MPs. The numbers simply aren’t there; and indeed as pre-eminent British psephologist John Curtice points out, there is no public clamour for another vote. “No deal” is not going to happen – May would face resignations, even Tory MPs abandoning the whip, if she seriously attempted it – and next week, Yvette Cooper’s amendment to block it is likely to pass.

So what’s left? In our tumultuous times, things can change dramatically: perhaps parliamentary arithmetic will swing dramatically behind May, perhaps a surge in support of a second referendum will happen, perhaps a majority of MPs will somehow back a sensible compromise such as Norway plus. Perhaps, perhaps, perhaps.

Or maybe May will decide that, rather than risk splitting her party, she has no choice but to call an election. She would claim that the political elite is trying to subvert the will of the people. It’s a possibility that Labour, and the broader left, need to prepare for. The only political calculation May has made that has paid off has been to absorb those who voted for Ukip in 2015: it is that which has given her an electoral firewall of up to 40% of the electorate, and that which means Tory defeat is not inevitable.

On Brexit, Labour will face unprecedented strains on its electoral coalition. It needs to avoid disillusionment leading to abstention or substantial defection among passionate remainers; but the electoral reality is that most of the Tory-held seats it needs to win voted leave. One possibility is that Labour commits to renegotiate a deal and hold a referendum on its terms, with a free vote offered to Labour ministers and MPs, just as Harold Wilson did in 1975. The other is simply to pledge to renegotiate a softer Brexit. Both have their risks.

Labour will have to put pressure on broadcasters not to frame the election as being about Brexit and nothing else. Even May, upon becoming prime minister, accepted that “burning injustices” led to the referendum result. Austerity, the fall in living standards, the housing crisis, struggling public services: all must be central to the debate, not just talk of customs unions and tariff-free access. After all, the next government may last for five years: it would be a travesty not to debate the full gamut of policy.

Corbynism’s success depends on being seen as an insurgent movement: Labour should be brave about picking fights with vested interests. Tory threats of Labour “chaos” will look absurd after the post-2015 turmoil, and with May dangling “no deal” as a serious prospect in an election campaign, Labour will have political space to be even bolder than last time. YouGov is alone in showing Labour significantly behind: the party should embrace such polls, casting itself as the underdog.

A viral social media campaign – so critical to bypassing a hostile media in 2017 – will be even more sophisticated this time around. On the ground, Momentum is already making plans for what it believes could be the biggest mobilisation of activists in the history of British democracy. Labour’s new community organising unit, led by London Citizens veteran Dan Firth, has given organising training to hundreds of activists in key marginals, built big campaign teams for prospective Labour candidates, and focused on embedding the party in previously neglected communities. An election will put this strategy to its ultimate test.

Sure, it may not happen. The fact that a senior Tory figure is leaking the party’s poor electoral prospects may be an attempt to scare backbenchers into voting for May’s deal; or it may be a sign that they fear she is going to roll the dice. Civil servants are certainly getting ready for a snap poll. Labour, and more importantly its supporters, must do so too. This could be the historic election that ends a generation of Thatcherite dogma, and builds an entirely new social model based on public ownership, workers’ rights, state investment and progressive taxation. They had better be prepared.

• Owen Jones is a Guardian columnist