Theresa May has held her position as prime minister since July 2016, but has promised her party's backbenchers that she will move on before the next stage of the Brexit negotiations, provided her deal passes through parliament.
As things stand, Britain will still leave the European Union on April 12 without a deal, a scenario many Conservative lawmakers would welcome, but that businesses fear could cause huge economic damage.
"It is also very hard now for Mrs May to bang on about Mr Corbyn being unfit to be prime minister when she has asked him to help her do the job".
The Taoiseach said that Prime Minister's offer to engage with the Labour leader on Brexit was "timely". Labour wants the U.K.to remain in the EU's customs union - a trading area that sets common tariffs on imports to the bloc while allowing free trade in goods moving between member states.
"There are members of her own party, hardline Brexiteers, who view the fact that she's having talks at all with Jeremy Corbyn as a form of Brexit betrayal", he said.
"I think the result will nearly certainly be, if Corbyn gets his way, that we remain in the customs union so that we can't control our trade policy, that there are huge areas of lawmaking we can't control, and Brexit is becoming soft to the point of disintegration", Boris Johnson, May's former Foreign Secretary, said according to The NYT. One minister quit on Wednesday.
Labour has called for the United Kingdom to remain closely aligned to the bloc's customs union and has committed to putting the results of any final deal to a public vote.
May will also be meeting with the first ministers of Scotland and Wales on Wednesday in her attempt to secure broad national support for her deal.
May has conceded that Britain will need a further delay to its departure in order to sort out the mess and avert a "no-deal" departure.
He was followed by junior Brexit minister Chris Heaton-Harris, who said in his resignation letter that the government "should have honored the result of the 2016 referendum" and left the European Union on March 29.
At a European Council summit on April 10, May will seek an extension to delay the departure until May 22, the day before the European Parliament elections begin.
"A no deal on 12 April at midnight looks increasingly more inclined", European Commission President Jean-Claude Juncker said Wednesday, adding that could bring disturbance for EU citizens and businesses, but much worse economic harm for Britain. It has become accepted Labour policy that any deal emerging from parliament should require popular approval in a confirmatory referendum (presumably, against the choice of remaining in the EU).
"The country needs a solution, the country deserves a solution, and that's what I'm working to find", May told lawmakers before meeting with Corbyn for about two hours.