The talks with Labour would continue at an official level on Wednesday, the spokesman said.
May met with Corbyn "to make clear our determination to bring the talks to a conclusion and deliver on the referendum result to leave the EU".
Brexit had been due to take place on March 29, but the deadline has since been extended to October 31 to buy the government more time to come up with a plan almost three years after British voters opted to leave the EU.
Parliament usually breaks for the summer in the second half of July, although the exact date has not been set.
That would mean Britain leaving the European Union on 1 August and the Prime Minister fulfilling her pledge to step down once the first phase of the Brexit process has been completed. "But the conversation at Cabinet wasn't about that".
"We are approaching the moment of truth", a cabinet minister said of the prime minister's decision, which effectively puts her premiership on the line.
They also said it was "imperative" that any exit plan be approved by Parliament before MPs go on their summer holiday, which normally begins at the end of July.
A Labour party spokesperson said Corbyn had raised "concerns about the prime minister's ability to deliver on any compromise agreement".
"You would have lost the loyal middle of the Conservative Party, split our party and with likely nothing to show for it", the letter said.
Number 10 sources insisted the Government would not sign up to a "permanent" customs union and any compromise position may only be an "interim" measure.
The signatories include Gavin Williamson, who she sacked as defence secretary, as well as potential leadership contenders Boris Johnson and Dominic Raab.
It is understood that, in the meeting with May tonight, Corbyn rejected any suggestion that Labour would support the withdrawal agreement bill without prior agreement. It would be followed by negotiations on a new trade deal with the EU.
"And, let's be absolutely straight, today hasn't helped".
"I talked to colleagues and some who voted for it last time now think it's dead and will vote against it this time".
He said the Tories "may well have to concede that there is a public vote of some sort" on the deal.
The Prime Minister is understood to have requested the meeting, and also dispatched her chief Brexit negotiator Olly Robbins to Brussels for two days of talks about the possibility of making changes to the Political Declaration to strengthen protections for workers rights and request a say in future European Union trade deals for the UK.