If May's deal still isn't able to command a majority in parliament, there's the immediate prospect of a no-deal Brexit on 12 April.
"This debate, this division, can not drag on much longer", said said from her Downing Street office.
Corbyn said he would be "very happy" to meet May and that he would set no limits ahead of the talks, while reiterating that his party aimed to keep a customs union with the EU, access for Britain to its single market and protections for workers.
They are trying to come up with a solution as Remainer MPs launch a new plot to stop a No Deal Brexit starting tomorrow - and following a warning from the country's top civil servant that crashing out of the European Union could push food prices up by 10 per cent and plunge Britain into a recession.
Speaking in Brussels, Barnier said there is still hope to avoid a so-called no-deal Brexit.
British Prime Minister Theresa May held crisis talks with her ministers Tuesday to try to resolve a months-long Brexit deadlock, as the European Union warned of the growing risk of disorderly departure from the bloc next week. "And we'll ensure that those are on the table", he said.
"This is a serious crisis and no-one can be pleased with what is happening in the United Kingdom currently", Barnier said. Pro-Brexit Brits, both in public and Parliament, believe too much independence has been given up to the European Union - particularly where it concerns border controls and immigration - and they want it back.
After an eight-hour cabinet meeting on Tuesday, Ms.
"I recognise my responsibility to represent the people that supported Labour in the last election and the people who didn't support Labour but nevertheless want certainty and security for their own future - and that's the basis on which we will meet her and we will have those discussions", Corbyn said. One participant said: "You can admire her suffering such ritual humiliation - it's nearly superhuman".
Almost three years since the United Kingdom voted to leave the European Union in a shock referendum result, it is still unclear how, when or if it will ever indeed quit the European club it first joined in 1973.
MPs were given slips of paper with eight options, free to opine on as many or few as they wished.
If she does manage to get her divorce deal across the line by the new April 12 deadline, it may be considered one of the greatest political achievements in the modern ear, or any era but based on everything that's happened so far it has a snowball's chance in you know where.
Following the ruling by Speaker John Bercow that any government motion must differ from the previous attempts, May separated the Brexit deal into its two components: the withdrawal agreement (a binding document dealing with divorce issues, citizens' rights, and the Irish border) and the political declaration (non-binding guidance for the next phase of negotiations on the future relationship).
The bill, presented by Labour's Yvette Cooper, will be debated on Wednesday.
The European Union's chief negotiator Michel Barnier said Tuesday that Britain's exit from the EU without a deal was becoming "day after day more likely".
"The deal is a deal which can appeal both to people who voted leave and to people who voted remain", he told the BBC.
Last week, Parliament took control of the process away from the government in order to hold a series of votes created to find an alternative way forward.
"It's up for London to say it, and to say it now".
The political chaos forced May to ask the European Union to postpone Britain's exit from the original date of March 29, but she is resisting delaying much longer.