She has promised to step down if her withdrawal agreement is passed by parliament and her overture to Corbyn has alienated some Conservatives still further.
"It is very disappointing that the cabinet has chose to entrust the final handling of Brexit to Jeremy Corbyn and the Labour party", said Boris Johnson, who led the Leave campaign in the June 2016 referendum. Labour wants the U.K.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.
Parliament has rejected the deal she negotiated with the bloc three times, with Corbyn's Labour consistently voting against it. Corbyn, who voted against joining the bloc in 1975, has said Brexit should include a customs union with the EU and protection for consumer and environmental standards and workers' rights. May said that if it fails to pass for a fourth time, the House of Commons would be given a series of votes to "determine which course to pursue". He said May wanted Labour "to bail her out of a position she's dug herself in".
The United Kingdom was supposed to leave the European Union last Friday but, almost three years after it voted by 52 percent to 48 for Brexit in a referendum, it is still unclear how, when or even whether it will quit the bloc it joined in 1973.
The Prime Minister will meet the Labour leader today and reportedly plans to hammer out a deal by Friday night to avoid a long Brexit delay and dodge European elections.
DExEU has faced seven ministerial resignations and one principle private secretary quitting their role in protest at Mrs May's hated Brexit deal.
We must deliver the Brexit the people voted for. But some Labour lawmakers who represent areas that voted strongly to leave the European Union not only reject this but also fear that such a "soft" Brexit would be seen as a betrayal.
Last month, the European Union agreed to postpone the original departure date of March 29, but gave Britain only until April 12 to pass a deal, come up with a new plan and seek a further extension, or leave without an agreement or a transition period to smooth the way.
Prime Minister Theresa May has announced what she intends to do next with Brexit.
"I recognise my responsibility", the leader of the left-wing Labour Party said.
"We're not setting any red lines for these discussions with the prime minister", she said. After that, he said, a short delay to Brexit would no longer be possible.
The Prime Minister's move to hold talks with the opposition angered some Brexiteers, with Wales Minister Nigel Adams resigning from his role. The deferred Brexit deadline will expire on 12 April.