British Prime Minister Theresa May met with the leader of the main opposition Labour party , Jeremy Corbyn, to seek a compromise aimed at getting her Brexit deal approved by lawmakers in the House of Commons. Both sides said that the meeting was "constructive" but "inconclusive."

If he is to agree to bail out May, Corbyn will require the Prime Minister to concede some of her red lines on Brexit. This is where things get interesting.

Labour wants to secure a permanent Customs Union with the EU, which would be considered a betrayal by many of May's Conservative MPs.

A large number of Corbyn's colleagues in the Labour Party also believe he should demand a heavy price for his support: A commitment from May to hold a "confirmatory" public vote on any deal that Parliament approves. In simple terms, a second referendum.

This is where things get even more interesting. Holding a confirmatory vote would require delaying Brexit. That would keep the UK in the EU beyond April 12. This matters, because it is the deadline for the UK to confirm whether or not it will take part in the EU Parliamentary elections -- something all EU member states are required to do.

A lengthy delay coupled with a commitment to a public vote raises a very important question: Would remaining in the EU be an option?

Senior members of Corbyn's team are in favor of it. Earlier in the day, Emily Thornberry, Labour's shadow foreign secretary, wrote a letter to her colleagues saying that "any deal agreed by Parliament must be subject to a confirmatory public vote, and yes, the other option on the ballot must be Remain."

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While Corbyn himself has been coy on a second referendum, it's popular among his MPs and his grassroots supporters. Backing a public vote would be consistent with Labour's Schrodinger's Brexit policy: It allows Corbyn to tell Europhile party members that he has kept the option of remaining in the EU on the table, while also committing to a Brexit deal to please Labour voters in areas that voted heavily to leave.

All of this, of course, might be hypothetical, as any extension to the Article 50 procedure -- the legal mechanism facilitating Brexit -- requires all of the other EU 27 member states to agree i t. But if last month's EU summit taught us anythi ng, it's that the EU under no circumstances wants the blame for a no-deal Brexit landing at its feet.

The political desire to stop a no deal isn't just confined to Europe. The mere fact that Theresa May has reached out to the Labour Party makes it clear that she would prefer a softer Brexit over a no-deal crash out.

As recently as last week, some sources close to the Prime Minister were spinning that she was gearing up for a no deal. But hardline Brexiteers have never forgotten that May backed Remain in the referendum and has surrounded herself with Remain-supporting allies.

The opposition to no deal was laid bare as the day's Brexit action closed. Members of Parliament finally took no deal off the table. The so-called Cooper Bill, named after the Labour MP Yvette Cooper who tabled it, passed the Commons, albeit by a single vote. The bill forces May to request an extension to the Article 50 process if she can't get her deal approved. MPs would then have to power to extend the endpoint of that request.

The government is losing control of Brexit. In an attempt to cling to power, May has made some enormous concessions. It has caused an almighty row in her party. Most hardline Brexiteer MPs are Conservatives. They see this week's events as an act of betrayal from a Prime Minister who is allowing the dream of Brexit to wither on the vine. The anger among her MPs is palpable. At the weekly session of Prime Minister's Questions, May faced hostile tongue lashings from her own Conservatives.

Brexiteer Julian Lewis asked: "Why is a Conservative prime minister who repeatedly told us that no deal is better than a bad deal, now approaching Labour MPs to bloackade WTO Brexit when most Conservative MPs want us to leave the European Union with a clean break in nine days' time?" His colleague, Caroline Johnson, followed up. "If it comes to the point that we have the balance the risk of a no-deal Brexit versus the risk of letting down the country and ushering in a Marxist, anti-Semite government what does she think at that point is the lowest risk," she asked, referencing the anti-Semitism crisis in the Labour Party.

Conservatives are furious that their Prime Minister is, in their view, selling them out and handing the keys of the country over to a man they believe to be a risk to national security.

But they may only have themselves to blame. As one remain-supporting Conservative MP explained to me earlier: "This is a group of people who ... having voted down the Withdrawal Agreement three times, are whinging that the Prime Minister is trying to seek a majority in Parliament. This isn't just an error, it's complete hypocrisy."