If MPs have not rallied round a deal by the summit, she has vowed to request a longer delay.
"I am very anxious that if we go into a long extension we might have an election, the pressure to revisit the question (of Brexit) increases, the whole thing becomes at risk, and also there's a massive political price", said another ex-minister.
The DUP's conditions "haven't softened" when it comes to the government's Brexit deal, Nigel Dodds has said.
"We always said that in terms of bringing a vote back for a third time we would need to see a shift from parliamentarians in terms of the support - I think that still is the case".
The 10 DUP MPs are viewed by Downing Street as crucial, not just for the votes they provide but the influence their stance has on Conservative Eurosceptics concerned about the Irish backstop.
Negotiations with the DUP were expected to continue on Monday, although Downing Street said a formal meeting has not been scheduled.
And by no means all eurosceptics will back their calls - others fear a long extension could risk Brexit and further destabilise a deeply divided and increasingly angry Britain, which voted 52-48 percent to leave the European Union in the 2016 referendum.
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It's the first part of a series and features Sonic , Amy, Shadow, and Eggman's team attempting to cross the line first. It's not exactly Gran Turismo, but the customization actually looks pretty deep for far a kart racer.
That would require the United Kingdom to participate in May's European elections and Mrs May warned it might result in Brexit never happening.
With time running out ahead of Brexit on March 29 and with no deal in place the Prime Minister is expected to ask the European Union for a Brexit extension when she visits Brussels later this week.
But he added: "There is an European Union summit this week".
On the other hand, UBS said that "success is far from certain".
Mrs May faces an uphill struggle to overturn the humiliating 149-vote defeat she suffered in her second attempt to secure backing for her plans.
Former Brexit secretary David Davis said her deal was "capable of rescue" if the negotiating strategy was changed with the alternative "a cascade of chaos".
But he added that a shift in the DUP's position would have a "big impact" and the implications of rejecting the deal for a third time weighed heavily on him "because it could lead to a general election, and we don't know how that will pan out".
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Plusieurs blessés sont aussi à déplorer. "Une opération de police majeure est en cours pour arrêter le tireur", a-t-il ajouté. Selon la radio-télévision publique NOS , le suspect avait comparu il y a deux semaines en justice dans une affaire de viol.
The Financial Times said May had been told by senior colleagues she will have to set a timetable for her departure if she is to persuading many rebels to support her deal.
Mr Dodds is also reportedly looking for a cut in air passenger duty, which is lower in the Republic of Ireland than Northern Ireland.
Ribble Valley MP Nigel Evans said Mrs May would have to go if there was a lengthy delay to Brexit.
"You're telling 17.4 million people who voted to leave that five years later you'll still be a member".
Ministers are continuing talks with Democratic Unionist Party MPs to bring them on board in the hope that dozens of Tories would follow suit.
It will be "a potent symbol of parliament's collective failure" if Britain ends up taking part in the European elections in May almost three years after voters backed withdrawal, she wrote in an article for the Sunday Telegraph.
Shadow chancellor John McDonnell said PM May risked "destroying confidence in our political system" if her government was planning to give DUP "another bung" Meanwhile, Labour leader Jeremy Corbyn has written to MPs across the Commons inviting them for talks to find a cross-party compromise.
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Around Christchurch, New Zealand and the world there have been vigils, prayers, memorials and messages of solidarity. "We are here to show Muslims are able to respond to them with a smart attitude", he added.