Labour leader Jeremy Corbyn called on the prime minister to "admit her strategy has failed".
"The Prime Minister, if she went through the lobbies for this tomorrow night, would be voting against the guarantees she has given in the Commons for months".
If a deal is made, parliament will make a second "meaningful vote".
Former attorney-general Dominic Grieve, said in the Times newspaper that a dozen or more government ministers could quit during the so-called high noon round of Brexit votes on February 27. "We do need as a parliament to hold our nerve, and we do need to send a clear signal to those in the European Union with whom we're discussing this deal", he said.
Defence Minister Tobias Ellwood told BBC Newsnight the ERG was a "party within a party. flexing its muscle" to take advantage of Mrs May's lack of a Commons majority.
If the motion is rejected, it would undermine May's efforts to show Brussels that if they do agree to renegotiate the Irish backstop, she has a stable majority in parliament who would approve the deal and other necessary legislation.
"Forty-two days out until Britain is due to leave, there is still divisions in a political party causing Ireland to spend hundreds of millions of euro to prepare for no deal".
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And Conservative vice-chairman Chris Philp said: "What a civil servant might speculate in a bar after a few drinks is frankly not that important". So perhaps it's best simply to lay out the current situation as simply and as objectively as possible and allow the reader to do the heavy lifting: last night MPs rejected the prime minister's negotiation position with the European Union, and a large swathe of her own MPs abstained because they don't trust what she tells them.
Asked whether she would resign if there was not a deal before the end of the month, Work and Pensions Secretary Amber Rudd said she planned to work with all colleagues to help the PM get her withdrawal agreement through Parliament.
The government lost in a 303 to 258 symbolic vote.
"If they supported this motion on Thursday, the Government would effectively be voting against their own expressed policy, as repeated in the House, including by the Prime Minister, on numerous occasions", the source added. He said: "People in the United Kingdom want certainty".
"It starts to bring into question whether in fact the Government is able to operate in the national interest at all". Earlier, ERG chairman Jacob Rees-Mogg said the vote was "not fundamentally important".
Greek foreign minister George Katrougalos told Today that Thursday's vote was "part of the contradictory message that we are receiving as the 27 from the UK".
However, some British Conservative MPs say a "no-deal" would be a better outcome than any form of a fragile agreement with the EU. "Miracles happen, but I cannot see what kind of miracle it is that could save the day".