For two years, Prime Minister Theresa May has tried to pilot the British state through a labyrinth of negotiations to get her country to quit the European Union without destroying either its economy or her party. On Monday morning, as some of her key cabinet ministers quit in a shocking mass resignation, she drove it into a cul-de-sac.

There now appears no way out for Ms. May: She cannot negotiate any workable Brexit deal, yet must deliver a departure from Europe. She cannot hold her party together around any coherent governing program, yet must remain Prime Minister. She is stuck in an endless circle of political self-destruction as her country tilts closer to the edge of the abyss, its economy frozen in anticipation.

It was the fundamental impossibility of Ms. May’s mission that caused Brexit minister David Davis, junior Brexit minister Steve Baker and foreign secretary Boris Johnson to resign in quick succession after a weekend meeting at the Prime Minister’s summer residence, Chequers.

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All three objected to Ms. May’s latest Brexit plan – which attempted to propose a negotiating strategy that would allow Britain to maintain its crucial trade ties to Europe – as too much of a compromise. For these ministers, and the rest of the party’s “hard Brexit” faction, the slim majority in the 2016 referendum was a call from British voters to end all relations with Europe, damn the consequences.

The fact that even Ms. May’s “Chequers” compromise would certainly have been rejected by the EU (which has the final decision on all deals), and the fact that the existence of a Britain-Europe border in Northern Ireland makes anything but a free-trade Brexit deal physically impossible, did not matter: For this half of the Tory party, any workable Brexit deal does not deserve the name “Brexit.” For the party’s other half, a hard Brexit would be unthinkable – and Monday’s exodus showed that the factions cannot be reconciled.

By provoking those angry departures, Ms. May appears to have triggered an unavoidable intra-party civil war between the fundamentalists and realists of Brexit – as with the Jacobins and Girondists of the French Revolution or the Bolsheviks and Mensheviks of 1917, theirs is a conflict that can only inflict irreparable damage on its own cause.

Ms. May is trapped in a paradox: Last year, without a plan, she triggered the EU constitution’s Article 50, which forces the 28-country bloc to expel Britain in March of 2019 (although the EU could extend the deadline). Yet, there is now no viable pathway to a deal (and even many of the hard-Brexiteers admit a “no-deal Brexit,” in which Brussels would cast Britain loose without any trade or institutional relationships, would be too economically devastating to imagine).

Donald Tusk, the former Polish prime minister who is president of the EU’s European Council and thus one of its chief Brexit negotiators, expressed hope that this civil war might entice Britain out of Brexit: “I can only regret that the idea of Brexit has not left with Davis and Johnson,” he wrote on Twitter. “But...who knows?”

Indeed, it has become increasingly clear to British voters and politicians that “Brexit” was a chimera, the product of dishonest fear campaigns, backed by questionable foreign-supported parties. Polls show a second referendum on Europe would receive a substantial “No” vote, and that few British voters now want their country to lose its economic ties to Europe.

The uncertainty is causing measurable damage. While most economists predicted Brexit would cause severe harm to the British economy and employment (because so many in the manufacturing and service industries use their UK operations to reach the far larger EU market), it has turned out that even the possibility of Brexit is hurting: The British Chamber of Commerce, in its quarterly report on Sunday, found the economy is sluggish, with companies having difficulty recruiting employees or signing contracts, and customers avoiding spending because of Brexit uncertainty.

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There were suggestions on Monday that Ms. May’s government could be on the verge of collapse – an event that would trigger the third election in three years.

But Ms. May is unlikely to depart soon, either by an internal Conservative Party leadership challenge or by a parliamentary confidence vote, in part because no popular figures within her own party seem willing or able to step up to the plate, and because the rest of her MPs fear the prospect of a loss to the Labour Party, itself almost terminally divided over Brexit.

As a result, Theresa May finds herself stuck in the exit door without a deal, without a stable cabinet, without a united message and without any viable way forward.