Rejecting the Brexit deal will be risky and lead to "division and uncertainty", Prime Minister Theresa May will say to MPs who oppose her plan.
Her Commons speech comes after the 27 other EU leaders approved the terms of the UK's exit at a summit on Sunday.
Mrs May now has to persuade politicians in the UK Parliament to back the deal.
But cabinet ministers admit she faces an uphill struggle, with Labour, the Lib Dems, the SNP, the DUP and many Tory MPs set to vote against it.
Northern Ireland's Democratic Unionist Party has said it will review its parliamentary pact with the Conservatives - which props up Mrs May's government - if the deal is approved by MPs.
Labour leader Jeremy Corbyn has said his party will oppose the deal, calling it "the worst of all worlds".
The prime minister has pledged to put her "heart and soul" into a two-week push to convince MPs to back the terms of the UK's withdrawal from the EU and its future relations with the bloc.
Parliament will decide whether to accept or reject the package next month, in a vote which is likely to be on 12 December.
Mrs May has said it is the "only deal" on the table for the UK, which is due to leave the EU on 29 March 2019.
Following a two-hour cabinet meeting earlier, No 10 said in the "unlikely event" that Parliament could not agree on the terms of withdrawal "all necessary action" would be taken to prepare the UK to leave without an agreement.
Mrs May's campaign - which saw her appeal to the public in a "letter to the nation" at the weekend - will later see Labour MPs briefed on the deal while there will be a reception for business leaders at Downing Street.
Every Labour MP invited to a briefing by PM's team on Brexit deal in the Commons tonight. Searching here, there and everywhere for support to get it through.— Nick Eardley (@nickeardleybbc) November 26, 2018
The Prime Minister will host a reception for over 100 business leaders in Downing Street this evening, including chief executives from manufacturing, retail, food and drink sector, financial services and trade associations — to sell her Brexit deal and take questions— Chris Mason (@ChrisMasonBBC) November 26, 2018
The Daily Telegraph reported Mrs May would challenge Mr Corbyn to a head-to-head debate. Labour says he would "relish" a debate while Lib Dem leader Sir Vince Cable said he would like to join in and "take them both on".
But former Conservative cabinet minister Damian Green said he was sceptical about the idea, telling the BBC's Victoria Derbyshire show it was unlikely to "illuminate" what was a hugely complex subject.
Why are some MPs saying they oppose the deal?
Opponents of the deal on either side of the argument say it fails to deliver on what people voted for during the 2016 referendum or what the public were promised during the campaign and afterwards.
Brexiteers argue that rather than taking back control, the UK is giving the EU too much of a say in key areas and hampering the UK's ability to strike trade deals with other countries.
In particular, they fear the UK could find itself trapped indefinitely in a "backstop" customs arrangement, designed to avoid the need for physical checks of people and goods at the border on the island of Ireland, without the unilateral right to exit.
Many Remain supporters argue the deal is inferior to remaining in the EU because it will not guarantee frictionless trade, while the UK will no longer have a say in setting rules and regulations it will have to abide by.
Those who want to stop Brexit say they want another referendum because, they say, in 2016 people did not know the detail of what Leave meant.
What is Theresa May's message?
In her Commons statement on Monday, Mrs May will say that backing the deal would bring an end to the uncertainty surrounding Brexit.
"Our duty as a Parliament over these coming weeks is to examine this deal in detail, to debate it respectfully, to listen to our constituents and decide what is in our national interest," she will say.
She will tell MPs to choose whether they want to back the deal and "move on to building a brighter future of opportunity" or reject it and "go back to square one".
On Sunday, Jean-Claude Juncker, the head of the European Commission, said anyone in Britain who thought the EU might offer better terms would be "disappointed" because this was the "only" deal.
But opponents of the deal say if it is rejected, EU officials would have to give ground to avoid a no-deal exit.
The DUP's Sammy Wilson said the EU was hoping Mrs May could "bludgeon" the deal through Parliament.
"But given it's been condemned by all sides, that's very unlikely and I think that Mr Juncker may finish up eating his words and having to look for an alternative arrangement," he told the BBC.
And the Leave Means Leave campaign group said Mrs May was seeking to "bribe or isolate" rebel MPs and the UK should not be alarmed by the prospect of leaving without a deal.
Analysis: 'No 10's carefully designed script'
By BBC political editor Laura Kuenssberg
No 10 is all too aware it is waging this campaign for its compromise against a wall of resistance.
There are doubts about elements of the deal inside cabinet, and the Tory backbenches are riddled with concerns.
The opposition parties and her supposed partners in government - the DUP - are all, so far, set against.
But the prime minister's chosen - and perhaps only realistic - political option at this moment is to keep pushing on with a deal that she believes allows us to leave the European Union without hurting the economy while putting the UK in charge of its own immigration policy.
There's irritation in government about the French president's warning over the long-term control of fishing rights.
Noises off from other EU leaders who tried in the main to show a helpful face in Brussels yesterday are not part of Number 10's carefully designed script.
The leaders of the remaining 27 EU countries have made clear they still hope to negotiate fishing access in UK waters based on existing rights.
At the EU summit, French President Emmanuel Macron warned that if, in future talks, the UK was unwilling to make compromises over fishing, the negotiations for a wider trade deal could be slowed down, which could potentially lead to the last-resort backstop plan coming into force.
But Brexit Secretary Stephen Barclay told the BBC it was not in the EU's interest, and countries such as France, for the backstop to be activated and there were "safeguards" to stop this happening.
"If you take quite literally what President Macron said, in the event of a backstop then all access to UK fishing waters would cease on day one so it is not as suggested," he told Radio 4's Today.
Shadow Brexit secretary Keir Starmer told BBC Radio 4's Today programme that if Mrs May's deal was voted down by Parliament, she would either have to re-negotiate or "there really ought to be a general election" because she had "failed so badly in these negotiations".
Analysis commissioned by the People's Vote campaign - which wants another referendum on Brexit - was carried out by the economic research group, the National Institute of Economic and Social Research, and claimed the deal would leave the UK £100bn a year worse off by 2030 than it would be if it had stayed in the European Union.
EU leaders approved two key Brexit documents at Sunday's summit: the 599-page, legally-binding withdrawal agreement which sets out the terms of the UK's exit, and also the political declaration which sets out what the future UK-EU relationship might be like.
If the agreement passes through the UK Parliament, it needs to go back to the European Council for a vote and then be ratified by the European Parliament.