May's dramatic shift left her caught between angry Conservatives who accuse her of throwing away Brexit, and Labour opponents mistrustful of her sudden change of heart.
Labour MP Paul Sweeney said May's outreach to his party "shows the desperation that she's in."
He said May wanted Labour "to bail her out of a position she's dug herself in."
The Prime Minister had recently held cross-party talks that went no-where.
May's pivot infuriated pro-Brexit Conservatives, who were seeking ways to stymie her plans.
Two junior ministers quit, and other MPs angrily accused May of putting Corbyn in the Brexit driver's seat.
Her new cross-party talks — after almost three years of seeking to push through her own version of a Brexit divorce deal — came amid EU warnings that a damaging withdrawal without a plan is growing more likely by the day.
After MPs three times rejected an agreement struck between the bloc and May late last year, the leaders of the EU's 27 remaining countries postponed the original March 29 Brexit date and gave the UK until April 12 approve the divorce deal or come up with a new one.
So far the House of Commons has failed to find a majority for any alternative plan.
"A no deal on 12 April at midnight looks more and more likely," European Commission President Jean-Claude Juncker said, adding that would bring disruption for EU citizens and businesses, but much worse economic damage for Britain.
EU Economy Commissioner Pierre Moscovici said a "no-deal" Brexit would mean long lines at borders and paperwork headaches for customs checks on the 11,000 vehicles entering and leaving Britain each day.
"I prefer strict controls at the price of a few lines of trucks to a health crisis or illegal trafficking," he said. "The security of Europeans will be our top priority."
May's pivot toward Labour points Britain toward a softer Brexit than the one she has championed since British voters decided in June 2016 to leave the EU.
Labour wants the UK to remain in the EU's customs union — a trading area that sets common tariffs on goods coming into the bloc while allowing free trade in goods moving between member states.
May has always ruled that out, saying it would limit Britain's ability to forge an independent trade policy.
May's decision to negotiate with Corbyn is risky for both the Conservatives and Labour, and could widen divisions over Brexit that run through both parties.
Labour is formally committed to enacting the voters' decision to leave the EU, but many of the party's MPs want a new referendum that could keep Britain in the bloc. They will be angry if the party actively helps bring about the UK's departure.
Pro-Brexit Conservatives say Britain must make a clean break with the EU in order to take control of its laws and trade policy.
Former foreign secretary Boris Johnson, a leading Brexiteer, said Brexit "is becoming soft to the point of disintegration." Ex-Conservative leader Iain Duncan Smith said he was "absolutely appalled" by May's talks with Corbyn.
Junior Wales Minister Nigel Adams quit his post, sending May a letter criticising her for seeking a deal with "a Marxist who has never once in his political life out British interests first" — a reference to Corbyn.
He was followed by junior Brexit minister Chris Heaton-Harris, who said in his resignation letter that the Government "should have honoured the result of the 2016 referendum" and left the EU on March 29.
Pro-EU MPs were not banking on talks between May and Corbyn succeeding.
They sought a legal lock to ensure May could not go back on her promise to seek a delay to Brexit rather than let Britain tumble out of the bloc.
A bill being debated today would compel May to seek to extend the Brexit process beyond April 12 in order to prevent a no-deal departure. Its backers hope to push the bill through into law before May attends an April 10 summit in Brussels where EU leaders expect to hear details of Britain's new Brexit plan.
EU leaders, weary of the whole Brexit circus, gave a cautious welcome to May's attempt at rapprochement.
German Chancellor Angela Merkel said she would work "until the last hour" to secure an orderly Brexit, but stressed that "these solutions have to be reached above all in Britain itself."
- AP
