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She said the "history books" would judge if MPs delivered on Brexit while safeguarding the economy and security.
But Jeremy Corbyn said the PM had "completely and utterly failed".
And the SNP said the PM was "in fantasy land and the government should stop threatening no-deal".
MPs will vote on the terms of the UK's withdrawal from the EU and declaration on future relations on Tuesday evening.
Labour and the other opposition parties will vote against the deal while about 100 Conservative MPs, and the Democratic Unionist Party's 10 MPs, could also join them.
Both Mrs May and Mr Corbyn met their backbenchers after the PM's Commons statement on Monday night - the PM to appeal once more for their support and the Labour leader to reiterate his plan to call for a general election if the deal is rejected.
Mr Corbyn also told his MPs a no-confidence vote in the prime minister would be "coming soon", according to BBC political correspondent Iain Watson.
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He added: "The time has come to place my loyalty to my country above my loyalty to the government."
Ahead of the vote, Mrs May briefed MPs on the controversial issue of the "backstop" - the fallback plan to avoid any return to physical Northern Ireland border checks.
She said her "absolute conviction" was that the UK and EU would be able to finalise their future relationship by the end of 2020, meaning the backstop would never be needed.
She published a joint letter from European Council President Donald Tusk and European Commission President Jean-Claude Juncker in which they stressed their "firm commitment" to working towards such an agreement - and said if the backstop were to be used it would be for the "shortest possible period".
However, they said they could not add anything to change the terms of the deal negotiated with Mrs May.
Quick guide: What is a no-deal Brexit?
Theresa May's government, and many others, believe this would be hugely damaging and want a more gradual withdrawal. But if Parliament can't agree on that, and nothing else takes its place, the UK will leave without a deal.
This would mean the UK would not have to obey EU rules. Instead, it would need to follow World Trade Organization terms on trade. Many businesses would see new taxes on imports, exports and services, which are likely to increase their operating costs. That means the prices of some goods in UK shops could go up.
The UK would also lose the trade agreements it had with other countries as a member of the EU, all of which would need to be renegotiated alongside the new agreement with the EU itself.
Manufacturers in the UK expect to face delays in components coming across the border.
The UK would be free to set its own immigration controls. However some UK professionals working in the EU and UK expats could face uncertainty until their status was clarified. The European Commission has said that even in a no-deal scenario, UK travellers won't need a visa for short visits of up to 90 days.
The border between Northern Ireland and the Irish republic would become an external frontier for the EU with customs and immigration controls, though how and where any checks would be made is not clear.
Some Leave supporters think that leaving without a deal would be positive if the right preparations were made. They say criticism is scaremongering and any short term pain would be for long term gain.
But critics - including both Brexit supporters and opponents - say that leaving without a deal would be a disaster for the UK: driving up food prices, leading to shortages of goods and gridlock on some roads in the South East resulting from extra border checks.