Senior Brexiteers launched a "kill zone" operation aimed at toppling the PM ahead of last night's confidence vote.
A group led by Jacob Rees-Mogg are now keen to press forwards – publicly urging Mrs May to resign as soon as possible.
But other Eurosceptics want to end the leadership drama and switch focus to forcing through a hard Brexit.
The two groups started openly rowing today in the wake of Mrs May's victory, which saw her win the support of 200 MPs with 117 voting against her.
And to make matters worse, Remainers have been openly taking potshots at the rebels.
Ex-Brexit Secretary Dominic Raab blasted: "It looks very difficult to see how this Prime Minister can lead us forward."
Mr Rees-Mogg, chairman of the European Research Group, called on the PM to tell the Queen she is stepping down.
He compared her to Margaret Thatcher, who resigned in 1990 shortly after winning a leadership vote by a narrow margin.
The Brexiteer told the BBC: "I think Theresa May should consider what she said last night.
"I agree with her that we do want somebody who can unite the country and the Conservative Party and she has to ask herself is she realistically that person?"
Richard Drax added: "I would suggest, were the Prime Minister thinking carefully this morning, she would offer her resignation and allow someone who can deliver this to take over."
And Peter Bone said: "It seems to me we need to have a leader who can unite the party and unite the country and deliver a proper Brexit."
But many of those who voted against Mrs May last night insisted they accept the result and are willing to back her leadership.
Arch Brexiteer Philip Davies told The Sun: “She’s won fair and square, we’ve had the vote and for me the leadership is settled."
Crispin Blunt said: “The leadership question is now behind us for a year and we must get behind Theresa May in delivering Brexit.”
Scottish Tory Ross Thomson, a close ally of Boris Johnson, added: "Let’s now come together. It’s time for colleagues to stop talking about leadership, to be gracious and to move on."
Even Mr Rees-Mogg's deputy Steve Baker called short of saying he wants to see the PM quit after her narrow victory.
Most of the biggest beasts such as Boris, David Davis and Esther McVey have kept their powder dry.
They are all strongly believed to have voted against Mrs May but have never said so publicly.
It's understood they don't want to be seen as leadership plotters – because it could kill off their chances of replacing Mrs May when she does leave office.
Iain Duncan Smith did confirm that he voted to get the PM out after deciding that was the only way to ditch her Brexit deal.
Yesterday senior ERG members co-ordinated the efforts to get a majority to vote against Mrs May.
Their office was nicknamed the "kill zone" as they plotted against her – although Mr Rees-Mogg insisted the tag was invented by opponents to discredit them.
Tory Remainers have hit out at the Brexiteers for trying to oust the PM.
Minister Alistair Burt blasted: "They never, ever stop. Votes against them, letters going in late – nothing matters to ERG.
"After the apocalypse, all that will be left will be ants and Tory MPs complaining about Europe and their leader."
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