Over a dozen Remainer Conservative MPs have said they will back a no-confidence vote to force the election if no deal was looking likely.
But Brexit supporters in the party are said to be urging Mrs May to decide to have the vote in early April, ensuring that Britain leaves the EU by the March 29 deadline – when no MPs will be sitting.
A Cabinet minister who supports the plan told MailOnline that attempting to thwart a no deal Brexit would ‘destroy the last bit of faith in politics’.
The minister said Remain ministers should simply quit if they don’t like no-deal, adding: ‘The Brexiteers who didn’t agree with the policy quit. They should do the same.’
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Any move for a General Election would be supported by Labour leader Jeremy Corbyn, who is set to say that a nationwide vote is the most ‘practical’ and ‘democratic’ way to ‘break the deadlock’ in Parliament over Brexit.
The Labour leader will argue that a government with a new mandate could negotiate a better withdrawal deal.
However, he has so far not backed calls for a second referendum – unlike Labour shadow Brexit secretary Sir Keir Starmer, who is reportedly backing calls for a ‘People’s Vote’.
Sir Keir is believed to have argued that an extension to Article 50 and a second referendum are the only viable options left to prevent a no-deal Brexit.
But Labour sources told The Times: ‘We have to take the parliamentary party with us and there are people who are nervous about a second referendum.
‘Keir is very clear that any policy has to command support regardless of his personal views.’
Despite Mr Corbyn’s desire for a General Election, Labour remain behind the Tories in recent opinion polls.
A poll of polls for 2018 also put Labour on 38% – just 1% behind the Tories, while Mrs May outscores Mr Corbyn on who would make the best PM.