A spokesperson for the party claimed they would "take the country forward" and "reset" negotiations with Brussels – should Mrs May fall, Sky News reported.
The Brexit deal on offer has caused uproar in the House of Commons over the issues of the Irish backstop.
At the moment it is estimated that around 100 Tory MPs are set to reject the deal, although Brexit Minister Kwasi Kwarteng said it "is a strong deal" and was confident in winning the vote.
Labour's John Tricket told Sky New's Sophy Ridge on Sunday that there should be a general election should Mrs May loose the vote on Tuesday.
He said: "Our preferred option, very, very strongly, is that we refresh the parliament.
"Though we are ready to form a minority government should that be necessary – and it could happen on Wednesday morning – and to begin to reset the negotiation and take the country forward in a much better direction."
Their statement comes after Conservative MPs Ester McVey and Boris Johnson brazenly threw their hats into the ring to replace the PM if she is outed in a few days.
But Mrs May has urged rebel Tories to back her or face loosing Brexit and the keys to No 10.
Who will run to be the next Tory leader and Prime Minister?
- Boris Johnson: Today refused to rule it out and quit the cabinet over Brexit. Wants to be more hardline with the EU and ditch the Northern Irish backstop.
- David Davis: Ex-Brexit Secretary made a bid to run to be Tory leader before but didn't get far. His experience in Government could give him the edge.
- Dominic Raab: Still wants to run even though his former mentor Mr Davis is too. Not as experienced as some other candiates in Government, and quit over the Brexit deal.
- Esther McVey: Said she could run if she was asked to by colleagues.
- Sajid Javid: Sounding out MPs about whether to back him.
- Amber Rudd: Jacob Rees-Mogg wants her to team up with a Brexiteer. Yesterday refused to speculate on whether she would run.
- Jeremy Hunt: Said to be interested in running.
The PM told them: "If you want Brexit, make sure you get it.
"When I say if these deal does not pass we would truly be in uncharted waters, I hope people understand that this is what I genuinely believe and fear could happen."
Mrs May signed off on a Brexit deal with Brussels last month after weeks on intense negotiation and has told MPs the only other option is a no deal Brexit – which would bring unknown consequences.
Her agreement will end free movement of people and allow Britain to strike it's own trade deals.
However the issues of a customs boarder between Norther Ireland and the Republic of Ireland has sown discord with MPs.
The backstop is intended to prevent a hard boarder between the two countries but could result in Britain staying in the customs union until another solution is found.
However, the deal is backed by Foreign Secretary Jeremy Hunt who has described it as the "best deal for British people".
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