Fudge is good only if it tastes sweet. Theresa May’s deal with the EU on Irish border trade is apparently too bitter for Ulster’s Democratic Unionist party to stomach. Yesterday they wielded a veto. A British government at an international summit was humiliated by a minority party pursuing a minority point of view. It is why governments should never rely on extremist parties. The DUP has three days to make amends, or a terrible vengeance should be taken on them.

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It does not matter that the DUP is hypocritical. Decades of Westminster indulging its political primitivism have come home to roost. Unionists have demanded separatism on education, trade, corporate taxes, abortion, homosexuality and a host of pet issues, yet they want to call themselves “British”. They are Irish.

Now the fiendish complexity of detaching the UK from the EU – on which question Northern Ireland voted remain – requires the DUP at least to honour the “all-Ireland economy”, which it accepted in the 1998 Good Friday agreement. The concept of “regulatory alignment” in yesterday’s deal should give it no practical problems, albeit possible administrative headaches. Objection appears to be one of principle: that the DUP wants a frictionless border, but nothing to make it different from a Brexit UK. It wants to square the circle. Like so much of international trade, that was always going to require fudge.

May must call the DUP’s bluff at once – and incidentally confront her own “rebel 50”. She must insist that it is this deal or the idiocy of the cliff edge. No deal has minimal support in parliament and in the country. Especially on worker migration, it would impose a massive economic burden on Britain, and on Northern Ireland a nightmare. A deal there must be. The backwoodsmen must be driven to the back of the wood.

Quick guide Why is the Irish border a stumbling block for Brexit? Show Hide Counties and customs Inside the EU, both Ireland and Northern Ireland are part of the single market and customs union so share the same regulations and standards, allowing a soft or invisible border between the two.

Britain’s exit from the EU – taking Northern Ireland with it – risks a return to a hard or policed border. The only way to avoid this post-Brexit is for regulations on both sides to remain more or less the same in key areas including food, animal welfare, medicines and product safety. The 'backstop' in Theresa May's Withdrawal Agreement was intended to address this - stating that if no future trade agreement could be reached between the EU and the UK, then rules and regulations would stay as they are. This has been rejected by Brexit supporters as a 'trap' to keep the UK in the EU's customs union, which would prevent the UK striking its own independent trade deals. There are an estimated 72m road vehicle crossings a year between Northern Ireland and the Republic of Ireland, and about 14% of those crossings are consignments of goods, some of which may cross the border several times before they reach a consumer. Brexit supporters say this can be managed by doing checks on goods away from the border, but critics say it will be difficult to police this without any physical infrastructure like border posts or cameras, which could raise tensions in the divided communities of Ireland.

Interactive: A typical hour in the life of the Irish border Photograph: Design Pics Inc/Design Pics RF

Now May must urgently call a meeting with the leaders of other parties in the Commons, and request assurances on a vote in favour of the Brussels agreement. In return she should form an all-party committee to monitor the ongoing talks. Party politics should be off the table for the duration. If Labour or others are unhappy with the eventual settlement, she can promise – or threaten – another referendum or an election. She might indeed have no option. For the DUP that could well drive them from majority status.

Now we see how damaging it is for Westminster to be choreographed for destruction rather than construction. Anyone can pick holes in May’s tactics and her strategy – including her denial of a customs union. Her failure to nail the DUP to the floor is costing her dear. But she must be given support from across the spectrum, when this is clearly in the national interest. A deal there must be with the EU. Northern Ireland cannot stop it.

• Simon Jenkins is a Guardian columnist