Like Britain’s schoolchildren, many of whom will be returning to their classrooms after the Christmas break, MPs will spend Monday reacquainting themselves with their friends and reluctantly returning their attention to work.

The task ahead of them is formidable – with Britain due to leave the European Union in less than 12 weeks’ time, parliament has neither approved an exit deal, nor put in place the necessary legislation to ensure a smooth departure.

Theresa May is hoping MPs have spent the fortnight’s break considering their duty to honour the result of the 2016 referendum, even if they don’t love every detail of her deal.

How will Theresa May be kicking off the new parliamentary term?

She’ll be away from Westminster, making a speech to launch the government’s 10-year plan for the NHS, which will underpin the £20bn-a-year increase in funding announced last summer.

The plan was delayed before Christmas, and some in government believe it is still not ready to see the light of day, but the prime minister is keen to highlight – both to the public and her own MPs – that she has other priorities to get on with, if they will just let her get Brexit out of the way.

When do MPs get back to talking about Brexit?

The House of Commons is due to begin debating the prime minister’s deal on Wednesday.

No date has yet been set for the meaningful vote, but May has indicated it will be Tuesday 15 or Wednesday 16 January. MPs will have to pass a motion before the debate begins, setting out how many days of discussion will be held.

There has been speculation of a fresh delay before the vote, as May seeks reassurances from the EU27 – in particular about the Irish backstop.

But time is already extremely tight to pass the legislation implementing the withdrawal bill, and to make other necessary changes. Delaying again would be an even more desperate measure than last month’s postponement.

Quick Guide Brexit and backstops: an explainer Show A backstop is required to ensure there is no hard border in Ireland if a comprehensive free trade deal cannot be signed before the end of 2020. Theresa May has proposed to the EU that the whole of the UK would remain in the customs union after Brexit, but Brussels has said it needs more time to evaluate the proposal. As a result, the EU insists on having its own backstop - the backstop to the backstop - which would mean Northern Ireland would remain in the single market and customs union in the absence of a free trade deal, prompting fierce objections from Conservative hard Brexiters and the DUP, which props up her government. That prompted May to propose a country-wide alternative in which the whole of the UK would remain in parts of the customs union after Brexit. “The EU still requires a ‘backstop to the backstop’ – effectively an insurance policy for the insurance policy. And they want this to be the Northern Ireland-only solution that they had previously proposed,” May told MPs. Raising the stakes, the prime minister said the EU’s insistence amounted to a threat to the constitution of the UK: “We have been clear that we cannot agree to anything that threatens the integrity of our United Kingdom,” she added.

Has anything changed?

May told Andrew Marr on Sunday that MPs could expect reassurances in the next few days in three areas: on Northern Ireland; on the role of parliament in future negotiations; and from the EU27 member states.

Downing Street is vehemently hoping to win over the 10 MPs of the Democratic Unionist party (DUP), as May promised she would try to do when she appealed to Tory colleagues to back her in the no-confidence vote last month.

But the DUP’s Sammy Wilson appeared implacable, in remarks made this week. “The withdrawal agreement, as currently proposed, flies in the face of the government’s commitments on Northern Ireland as we leave the EU,” he said.

The DUP’s deputy leader, Nigel Dodds, said the backstop provision remained the “poison” affecting any vote on the withdrawal agreement in the House of Commons. “Theresa May still insists that what she has negotiated is a good deal. She should remember that it would already have been consigned to the bin but for her pulling the vote in December.”

Germany and Ireland have been consulting closely in recent days on a joint plan to offer the prime minister a helping hand, including by extending the non-legally binding political declaration to include promises that the Irish backstop will never need to be used. Jean-Claude Juncker has also been closely involved in seeking a compromise, speaking directly to May.

However, Brexit-watchers report a reluctance to offer significant concessions before the deal has been voted down. “There is a desire in Brussels to leave the final concessions until the very last minute, so it is too late for Eurosceptics to demand more,” says Mujtaba Rahman, of the consultancy Eurasia Group.

Arlene Foster and Nigel Dodds of the DUP. Theresa May will need to secure the party’s votes. Photograph: Stefan Rousseau/PA

What happens if the vote is lost?

That depends partly on the margin of defeat. If it is less than, say, 100, the government may hope it can have one last go at winning something extra from the EU27, and then come back to the Commons for another roll of the dice.

Parliamentary convention would make that difficult, as it suggests a government cannot simply table the same motion repeatedly in the hope of winning it; but substantive enough concessions might allow May to argue she is asking MPs to consider a different proposition.

Labour is likely to table a vote of no confidence in the government, though it is unclear whether it would do so immediately – and even less unclear whether it could win it.

Jeremy Corbyn has said Labour’s approach would then be to try to force May to pursue a different approach to Brexit – in particular a permanent customs union.

Pressure on May from inside the cabinet would also intensify – though her ministers are themselves divided, with Penny Mordaunt and Andrea Leadsom advocating a “managed no-deal”, at one end of the spectrum, and Amber Rudd, at the other, willing to countenance a second referendum in the face of deadlock at Westminster.

Downing Street still hopes to convince MPs – perhaps at second time of asking – that they face a choice between her Brexit, no deal, or no Brexit.

And if they can win over the DUP, they hope less hardline Tory Leavers will follow; Labour MPs in Leave-leaning seats might swing behind her too, if the only other option appears to be no deal, or ditching Brexit altogether.

What if she loses again?

A crushing defeat next week, or a second loss later in the month (as the stopwatch runs down towards 29 March) would amount to a major political crisis, with the government simply unable to get its deal ratified.

What would happen next is anyone’s guess. May could herself decide to pull the emergency cord and call for a referendum, or a general election – though both would require extending article 50, which in turn demands the agreement of the EU27.

The prime minister could try to test the will of MPs for alternative options, through a series of so-called indicative votes – though there is scant enthusiasm for that idea in No 10.

She could even tack towards centrist Tories and the Labour frontbench, by shifting towards a permanent customs union. The House of Lords will consider the trade bill on 21 and 23 January, which crossbench peers hope to use as another opportunity to force the issue.

With time running out, May could even face a mass cabinet walkout, aimed at persuading her to step aside and let a successor take on the unenviable challenge of ramming Brexit through a hung parliament.

And meanwhile, MPs advocating alternative approaches – whether Labour’s own closer, Norway-style relationship or a second referendum – will seize the opportunity to ramp up the pressure, using every parliamentary tactic they can think of.

As the prime minister herself said, if the deal is rejected, “we are going to be in uncharted territory”, but there is little evidence as yet that the Christmas break has shifted the dynamic in Downing Street’s favour. As one sardonic Whitehall source put it on Sunday, “it’s almost as if changing nothing and telling MPs to go and have a think isn’t a strategy”.