LONDON — The U.K.'s Labour party has a problem.

Make no mistake: underneath the gloved hand of friendship extended to its leader Jeremy Corbyn by British Prime Minister Theresa May on Tuesday was a clenched fist primed to punch the opposition party right where it hurts.

For almost three years, the Labour leader has performed a careful balancing act to keep his party united: supporting Britain’s withdrawal from the European Union in principle while opposing the version negotiated by the prime minister.

The calculation is simple. Labour supporters are overwhelming opposed to Brexit, but the constituencies it needs to take power are overwhelmingly in favor. The leadership does not believe it can afford to be either purely anti-Brexit or purely pro.

May’s offer to the Labour leader to help shape Brexit is designed to finally push Corbyn from his high-wire tightrope walk.

“I’m really depressed about it [...] It’s a good move for her. It forces us to choose." — Labour MP

The prime minister wants the Labour leader to decide. Is Labour a soft Brexit party or a second referendum Remain party?

Whichever way Corbyn jumps he risks alienating a significant chunk of his party, both in parliament and in the country at large.

“I’m really depressed about it,” said one Labour MP on condition of anonymity. “It’s a good move for her. It forces us to choose.”

The Labour MP said that if Corbyn is seen as facilitating Brexit, a significant chunk of Labour’s parliamentary party could walk away to join the new Change UK/Independent Group of MPs, which opposes any British exit from the EU.

“If he doesn’t commit to the principle of a second referendum it will be chaos,” the MP said. “He cannot dig [the prime minister] out of a hole. He just cannot.”

But should Labour hand May the numbers to get a Brexit deal through the Commons, the party could implode, jeopardizing its chances of winning the next election whenever it comes.

In the second round of indicative votes in the House of Commons on Monday, 203 Labour MPs voted for a second referendum and 121 for article 50 to be revoked if the country was heading for no deal.

Labour party members are also overwhelmingly opposed to any form of Brexit.

At the same time, if Corbyn were to back a second referendum he would also risk seeing a chunk of Labour MPs representing “Leave” seats moving to back the prime minister’s deal in the final showdown next week.

Underneath the parliamentary shenanigans, is a game of chicken between the two parties — and one that is potentially existential to both.

The Conservative government cannot give up on Brexit. Labour cannot give up on bringing the whole thing crashing down to force an election.

The spoils go to whoever wins this struggle.

The problem in games of chicken is it is winner takes all.

Responding to the prime minister on Tuesday, Corbyn sought once again to thread the needle. He declined to put up any red-lines which could be construed as blocking Brexit. But also did not demand a second referendum.

He said Labour wanted a customs union with the EU, “access” to the single market and protections of workers rights, consumer standards and environmental regulations. He did not demand a second referendum.

During prime minister’s questions Wednesday, the former Labour leadership candidate Owen Smith aimed a warning shot at Corbyn, declaring Labour’s policy on Brexit was “to secure membership of the customs union, the single market and — crucially — to get a ‘people’s vote’ on any deal.”

Before the prime minister’s last attempt to push through her divorce deal, on March 29, the leader of Momentum, Jon Lansman, tweeted a warning to any Labour MP thinking of backing the deal. “Any Labour MP who votes today with the Tories to leave the EU with absolutely no idea where we are heading does not deserve to be a Labour MP.”

This is just a taste of the vitriol which would descend on any Labour MPs which handed the prime minister victory, undermining the prospect of a general election.

The problem in games of chicken is it is winner takes all.

But if neither side swerves, almost anything could emerge from the mess.