Theresa May last week won a vote of confidence from Conservative MPs. Under party rules, she cannot be formally challenged again for another 12 months. But this does not mean she is safe. Jeremy Corbyn is moving a vote of no confidence in her. There are other, more informal, ways in which either the cabinet or Conservative MPs can indicate that they seek an alternative leader. In her party, the leader leads and the party follows, except when the party decides not to follow. When that happens, the leader ceases to be leader.

Jeremy Corbyn also threatens a no-confidence vote in the government that if carried means, under the terms of the Fixed-term Parliaments Act, a general election – unless an alternative government can be formed within 14 days. But, even if such a vote is not carried, the prime minister still needs to be able to command the confidence of the Commons on major policies such as the withdrawal agreement. If that is lost, while there is no constitutional requirement for a prime ministerial resignation or election, the prime minister may nevertheless come to find her position untenable.

But these constitutional and political shenanigans are hardly relevant to the crisis that Britain now faces. It would indeed be paradoxical were May to be overthrown by the Commons, since her deal probably has more Commons support than the alternatives of no Brexit or no deal. If she were defeated, it would be by a coalition of incompatibles – Tory and DUP Brexiteers who believe that she has aligned Britain too closely with the European Union – and Labour, Liberal Democrat, SNP and perhaps a few Tory remainers who seek either a closer alignment with the EU or a second referendum. Clearly this coalition of incompatibles would be unable to agree on any alternative policy. So a new prime minister, almost certainly a Conservative, would face exactly the same problems as May. That means a general election. But there is no reason to believe that an appeal to the people could resolve the parliamentary deadlock any more than the 2017 election did.

The irony is that there is a much greater consensus among MPs than is apparent from the posturing of May’s opponents. Kenneth Clarke believes that about 80% of MPs are against a no-deal Brexit, while nearly all MPs accept that there should not be a hard Irish border, which would be incompatible with the spirit of the Good Friday agreement of 1998.

The withdrawal agreement achieves both of these aims. It meets two essential requirements that almost all MPs support – that, if no future relationship with the EU is agreed by the end of December 2020, there should be no hard border on the island of Ireland and no border in the Irish Sea, with full access for Northern Ireland businesses to the UK internal market. The agreement therefore protects both the north/south strand and the east/west strand of the Good Friday agreement.

The agreement does, admittedly, require Northern Ireland to ensure that its regulations are in conformity with those of the EU in those limited areas of the economy necessary to avoid a hard border and protect north/south cooperation under the Good Friday agreement, such as agricultural products, veterinary controls, state aid rules, VAT and excise in respect of goods. But these constitute a small fraction of the single market rules that currently apply. If, during the period of the backstop, Britain decides to adopt different regulations from those of the EU, there would be limited checks, not on trade from Northern Ireland to the rest of Britain, but from Britain to Northern Ireland.

There is already, of course, considerable differentiation between Northern Ireland and the rest of the UK – different regulations on animal health and agricultural products, not to speak of different rules on abortion and same-sex marriage. Northern Ireland has also committed to a introducing a different corporation tax rate from the rest of the UK. The DUP is happy to accept differentiation where it is in that party’s interests. But differentiation is very different from a border in the Irish Sea and, in return for a limited degree of compliance with EU rules, Northern Ireland gains both the benefits of the UK internal market and of the EU internal market. Economically, it is a good agreement for the province.

No doubt it is for this reason that the deal has been welcomed by almost all the Northern Ireland parties except for the DUP, including the unionist biconfessional Alliance party, and by the Northern Irish business community. In opposing the agreement, the DUP is not only failing the people of Northern Ireland. It is unilaterally breaking the confidence-and-supply agreement with the Conservatives, which declares unconditionally that the party “agrees to support the government on legislation pertaining to the United Kingdom’s exit from the European Union”. The agreement is for the length of the parliament and can only be reviewed by the mutual consent of both parties. In return for that, Northern Ireland received £1bn of public money. The DUP, therefore, is in breach of contract and arguably guilty of taking public money under false pretences.

Labour, too, is hypocritical in opposing the deal since its policy is to keep the UK in a customs union with the EU. There is now no time to negotiate any new arrangement, whatever that may be, since there is little consensus on the Labour front bench, even were the EU willing to contemplate one.

But the Conservative Brexiteers and DUP, who seek to defeat Theresa May, are guilty of far worse. For the most likely alternative to the deal is a no-deal Brexit. Even if we ignore alarmist talk about aeroplanes being grounded and medicines being unavailable, there would be, on 30 March, customs duties and a host of complex regulations for companies exporting to the EU. That means bankruptcies and unemployment.

Conservative Brexiteers and the DUP, instead of plotting to engineer a constitutional crisis, would be better employed during the Christmas period explaining to their constituents why they are adopting a stance that will put many of those who elected them out of work. This is the central issue that should be concentrating minds at Westminster.

• Vernon Bogdanor is professor of government at King’s College London. His book Beyond Brexit will be published on 7 February

Theresa May pushes forward £2bn no-deal Brexit preparations Read more

• This article was amended on 20 December 2018. An earlier version referred to “Northern Ireland and the rest of Britain”, which has been corrected to “Northern Ireland and the rest of the UK”.