Equally, her fate could be sealed if her plans are rejected for the fourth time by MPs in June.
"What she (May) is working to do is to get a deal passed as soon as possible", the spokesman said.
A Downing Street spokesman said last night's talks between Mrs May and Mr Corbyn were "both useful and constructive" and senior figures from both parties would meet again today.
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.
Allies of the Prime Minister attempted to calm Tory fears about the prospect of a damaging split in the party over a customs union - Labour's key demand in the talks.
No date has been set for the summer recess, but Parliament usually rises near the end of July.
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.
She turned to Labour last month in the hope of finding a way through, but the party is insisting on a close trading relationship with the European Union that many Conservative MPs reject.
"In particular he raised doubts over the credibility of government commitments, following statements by Conservative MPs and Cabinet ministers seeking to replace the prime minister", his spokesman said.
"We believe that a customs union-based deal with Labour will very likely lose the support of Conservative MPs, like us, who backed the Withdrawal Agreement in March (in many cases very reluctantly), and you be unlikely to gain as many Labour MPs to compensate", they said.
"No leader can bind his or her successor so the deal would likely be at best temporary, at worst illusory", said the letter, whose signatories included Gavin Williamson, who was sacked as defence minister this month, and former foreign minister Boris Johnson.
"I talked to colleagues and some who voted for it last time now think it's dead and will vote against it this time".
Meanwhile, Mrs May's chief negotiator Olly Robbins was in Brussels for two days of talks about the possibility of making changes to the Political Declaration - the document setting out the framework for the future UK-EU relationship after Brexit.
British PM Theresa May will have to get a Brexit deal through parliament before the summer break.
Following the meeting, a Downing Street spokesman said: "We will... be bringing forward the withdrawal agreement bill in the week beginning the 3rd June".