May, who will close Tuesday's debate, now hopes her Tory party will say clearly what it wants to change in the deal she's struck with the EU.
"I also accept that this House does not want the deal I put before it, in the form that it now exists".
"I think we should send the Prime Minister back to Brussels with a strong mandate to be able to say if you compromise with us on this one issue, on the backstop, we would be able to a get an agreement - an agreement that is nearly there", he told BBC Radio 4's Today programme. By that time, it'll likely become clear whether Brexit will be paused, possibly indefinitely, or whether the embattled prime minister will be sent back to Brussels for more talks with the EU.
The EU has so far ruled out reopening the Withdrawal Agreement, which May said would be needed to provide legal changes to the so-called backstop, an insurance policy to prevent the return of a hard border in Ireland.
Prime Minister Theresa May addressing the House of Commons.
Brexit hardliners from May's Conservative Party are set against the deal due to the backstop, which could see Britain indefinitely tied to European Union trade rules in order to keep open the border with the Republic of Ireland. That ended controls along the 500-km (300-mile) land border and set up all-Ireland rules and institutions that make Northern Ireland special within the United Kingdom.
Parliament rejected Prime Minister Theresa May's Withdrawal Agreement, which includes a almost two-year transition period to help minimise economic disruption, earlier this month.
Tuesday's House of Commons debate on the Government's European Union withdrawal deal will be opened by Brexit Secretary Stephen Barclay and closed by the Prime Minister.
Opposition Leader Jeremy Corbyn said the Parliament's first duty was "to block a disastrous no deal", and he believed that, whatever the outcome over the coming weeks, it was inevitable the government would have to delay Brexit, as there was not enough time to pass the necessary legislation.
Asked if that position would change if MPs vote to demand changes to the Irish backstop, Mr Schinas said: "The only thing I have to say is that we shall wait for the result of the vote of the Commons tomorrow".
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He told "Today" that any alternative arrangement would have to be "legally binding" as "I don't think anybody is going to accept something which is just warm words". "We need to go back into the text of the treaty and solve the problem".
But the chairman of the ERG, Jacob Rees-Mogg, said its members, thought to number at least 60, will not support the scheme.
The small Northern Irish party which props up May's minority government but opposes her deal, said the contents of May's speech to lawmakers on Tuesday will determine whether it will support the amendment.
Alison McGovern MP, a leading supporter of People's Vote, said that parliament "will continue to be gridlocked and the only way forward now is a public vote".
Five other amendments, including Labour MP Yvette Cooper's bid to delay Brexit if Mrs May does not get her deal through Parliament, were defeated.
Opposition to the backstop by pro-Brexit politicians - who fear it will trap Britain in regulatory lockstep with the European Union - helped sink Mrs May's deal on January 15, when Parliament rejected it in a 432 to 202 vote.
If a subsequent piece of legislation is passed, it would give May until February 26 to get a deal approved by Parliament or face a vote on whether to ask the European Union to delay Britain's exit to avoid leaving without a deal on March 29.
In a separate development, there was a glimmer of hope for remainers as a majority of MPs voted for a amendment calling for May to refuse a no-deal exit.
Ms Cooper said the PM was heading for a "blindfold Brexit where nothing is resolved".