Mrs May faces a vote of no confidence on Wednesday after suffering a massive parliamentary defeat over her controversial EU withdrawal agenda.
Labour launched a bid to oust the Government after Mrs May's Withdrawal Agreement was overwhelmingly rejected by 432 votes to 202.
Despite the humiliating defeat, Government sources remained optimistic about seeing off the Labour challenge after the Democratic Unionist Party (DUP) and leading figures from the Brexiteer and Pro-Europe wings of the Tory party said they would back the PM.
The scale of the 230-vote rejection of the Government's Brexit agenda saw Mrs May pledge to reach out to leading parliamentarians from across the Commons to try and find a way forward.
With the UK scheduled to exit the EU in just over 10 weeks' time on March 29, the Prime Minister has until next Monday to return to the Commons and present a "Plan B" option.
After suffering the the biggest government defeat on a meaningful vote for at least a century, which saw 118 Tory MPs rebel, opponents of the PM's Brexit stance insisted Downing Street must now show real movement.
Calls for Article 50 to be extended, meaning the UK remains in the EU longer, also intensified among pro-Europeans.
Mrs May signalled she hoped to find "genuinely negotiable" solutions that she can hammer out with Brussels after the defeat.
However, French president Emmanuel Macron made it clear a renegotiation of the Brexit deal was unlikely.
Speaking after the Commons vote, he said: "I don't really believe in this, because we already went as far as we could."
The Yorkshire Post says: Who now governs Britain as Theresa May humiliated?He told British leaders to "figure it out yourselves" as he wished them "good luck" as he predicted that Britain would ask for more time to hold talks.
The comments came as it emerged Chancellor Philip Hammond and Business Secretary Greg Clark used a private telephone call to tell business chiefs not to expect changes to the legal Brexit withdrawal text, but rather to the political declaration on future relations with the EU, according to Government sources.
The Financial Times, meanwhile, reported Mr Hammond told those on the call the Government would not put any "obstacles" in the way of a plan by Tory MP Nick Boles to give senior backbenchers a role in finding a solution to the deadlock.
"We have to reach out to MPs in the Commons first," the Chancellor is reported to have said. "There is a large majority in the Commons that is opposed to no-deal."
But, Mr Corbyn's hopes of forcing an early general election were dampened as the DUP Westminster leader Nigel Dodds said his party would back Mrs May.
He told BBC2's Newsnight: "We will be supporting the Government in the no confidence motion.
"What it really shows is when it comes to the crunch and the Government's survival is on the line the DUP will be able to keep the Government in power."
Asked if Labour could win Wednesday's no confidence vote, shadow international trade secretary Barry Gardiner told the BBC: "I think the numbers are probably not there tomorrow. We will hope that we can."
Mr Gardiner refused to be drawn on reports that up to 100 Labour MPs were set to call on Mr Corbyn to pivot towards a second Brexit referendum on Wednesday.
European Commission president Jean-Claude Juncker, who had cancelled travel plans in order to be in Brussels for the aftermath of the vote on Wednesday, voiced "regret" at the defeat of what he termed "the best possible deal".
He said the Commons vote "increased the risk of a disorderly withdrawal" from the EU.
Mr Juncker said: "I urge the United Kingdom to clarify its intentions as soon as possible."