But Mrs May also made it clear she would first need to know if the numbers were there for any resignation pact before she agrees to ponder it any further.
He is now leading delicate behind the scenes efforts to try to talk round diehard Brexiteers to agree to the deal that could end the four month Brexit logjam that has paralysed Westminster.
But with trust between the arch-Brexiteer 60-strong European Research Group and No10 at an all-time low, many of their Tory MP diehards are insisting on a public declaration from Mrs May first.
The Ulster unionists have also signalled to allies that they too are ready to back the PM’s EU agreement, but only at the last minute once the ERG have said they will.
A senior Tory Brexiteer told The Sun: “It’s a tree way Mexican stand-off.
“There is a way through all this if everyone jumps at the same time - the PM, the ERG or the DUP.
“But nobody wants to be the first to move.”
The senior figure added: “The problem is we know how Mexican stand offs usually end”.
The dramatic development emerged as Westminster came close to boiling point as MPs fought over Brexit’s fate.
In a disaster for Mrs May, Parliament succeeded in a dramatic bid to seize control of Brexit.
Her Government was defeated by 329 v 302 votes in in the Commons by a backbench plot to take control of the agenda on Wednesday to hold a series of indicative votes.
Whatever Brexit alternative MPs pick could then be turned into law next week, from a softer deal to a second referendum.
They were Health minister Steve Brine, Industry minister Richard Harrington and Foreign Office Minister Alistair Burt.
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The PM pulled another planned vote on her exit deal planned for Tuesday after telling MPs there is still not enough support for it among them.
She ignited a fresh uproar with Tory Leavers by ruling out a No Deal Brexit without the House of Commons’ say so.
Parliament seized Brexit control last night — with MPs backing “indicative votes” on options tomorrow
More than 100 Tories are ready to back a Norway-style soft Brexit if MPs win the right to choose a different type of Brexit, it was claimed.
Mr Duncan-Smith has told fellow Brexiteers that he thinks it’s vital Mrs May “should be allowed to go with dignity”.
But the ex-Tory chief’s bid to broker a grand deal sparked a major split in the ERG, as others – lead by the group’s deputy Steve Baker- insisted they would still hold out.
Another senior ERG member told The Sun: “We will not agree to any deal with her going, because we cannot trust her to go through with it.
“She will recant the moment she gets her EU agreement through the house.”
The senior trio of Boris, IDS and Mr Rees-Mogg believe a new Prime Minister would salvage their hopes of less ties to Brussels by carrying out a negotiation for a different trade deal than Mrs May’s vision.
Their switch would bring potentially dozens of other Tory ERG members with them, putting Mrs May’s deal within touching distance of passing.
Pledge on open border
LEO Varadkar says he is confident a solution can be found to keep an open Irish border even if there is a No Deal Brexit.
But the Irish PM warned any fix would look a lot like the proposed backstop, with Northern Ireland treated differently on customs and regulation.
He said: “The UK Government has already indicated that in the event of No Deal the first thing they will do is treat Northern Ireland differently in terms of customs. That’s what will be required essentially.”
The Taoiseach shrugged off fears of border delays in the event of a No Deal. He said: “I’m still confident and I still think it’s likely we will have a deal.”
His remarks came as EU officials revealed they were in “intense discussions” with Dublin over how to deal with the border if there’s No Deal.
Eurocrats say they will make Britain accepting a backstop-style fix the first condition of opening post-Brexit trade talks.
Meanwhile, Ireland’s stance on the border is undermining support for Theresa May’s deal.
DUP Brexit spokesman Sammy Wilson said: “The Irish Government has made it quite clear they have no plans whatsoever to put any infrastructure along the border.
“Yet the Withdrawal Agreement is predicated on the view that it’s unavoidable. The EU’s bluff has been called on this.
“Why would the Prime Minister ever expect us to support an agreement based on a lie?”
Despite swirling plots, No10 publicly refused to discuss any plans for Mrs May’s resignation yesterday.
The PM’s official spokesman said: “I don’t think it’s a matter for me to discuss with her”.