Leader Arlene Foster told RTE News talk of a Northern Ireland-only backstop was “far off the mark”.
Earlier, Mr Rees-Mogg told MPs: “The events that may require that Saturday sitting have not yet reached their fruition.”
Despite the EU’s chief Brexit negotiator Michel Barnier this morning declaring a Brexit deal is “still possible this week”, he was said to be demanding a legal text be agreed by the end of Tuesday in order for an agreement to be approved by EU leaders by the weekend.
Briefing foreign ministers from the remaining 27 EU member states, Mr Barnier was said to have told them the latest UK proposals were not yet good enough.
Without a legal text by the end of today, Mr Barnier was said to have told EU ministers he was likely to recommend more negotiations will be needed beyond this week’s Brussels summit.
Luxembourg’s foreign minister Jean Asselborn said: “There is some optimism, he [Mr Barnier] is trying for a deal tonight.
“Otherwise, we will most probably need another summit later this month.”
Belgium’s deputy prime minister, Didier Reynders, said: “If we have an agreement tonight it will be possible to go to the Council, and then again to the British parliament. But it’s not easy. We have some red lines. They are well known by all the partners.
“And I am hoping that it will be possible today to make some progress.”
Asked if there would be another emergency EU summit if necessary, Mr Reynders said: “There are many possibilities.
“But if it’s possible we want to conclude today and then have a normal European Council. If it’s not we will see.”
Earlier, speaking on his arrival at the gathering of EU ministers in Luxembourg this morning, Mr Barnier told reporters: “Our team are working hard.”
“This work has been intense all over the weekend and yesterday.
“Because, even if an agreement will be difficult – more and more difficult, to be frank – it is still possible this week.”
He added: “Reaching an agreement is still possible. Obviously any agreement must work for everyone – the whole of the UK and the whole of the EU.
“It is high time to turn good intentions into a legal text.”
Issues over customs, consent for Northern Irish parties and so-called level playing field commitments are said to remain in EU-UK negotiations.
Mr Barnier’s comments prompted the pound to climb by nearly a cent against the dollar to nearly $1.27, and also spike by almost a cent versus the euro to €1.15.
Downing Street did not engage with reports of a midnight deadline for a legal text.
The prime minister’s spokesman told reporters in Westminster: “I will simply say we want to make progress towards securing a deal as soon as possible and we want to make progress ahead of the EU council summit on Thursday.”
The spokesman also revealed Boris Johnson had a “constructive” phone conversation with French President Emmanual Macron this morning.
As he arrived at Tuesday’s meeting in Luxembourg himself, Brexit Secretary Stephen Barclay said: “The talks are ongoing, we need to give them space to proceed but detailed conversations are under way and a deal is still very possible.”
Mr Barnier’s assessment of the state of Brexit talks contrasted with Finland prime minister Antti Rinne’s view on Monday.
Mr Rinne, whose country currently holds the EU’s rotating presidency, claimed “there is no time in a practical or legal way to find an agreement before the EU Council meeting,” adding: “We need more time.”
Meanwhile, the prime minister was told he will find it “very, very challenging” to get a Brexit deal through parliament before the current 31 October deadline.
Former foreign secretary Jeremy Hunt, the runner-up to Mr Johnson in this year’s Conservative Party leadership contest, poured cold water on the prime minister’s vow to “get Brexit done” by Halloween.
He also raised the possibility of Brexit being delayed by “a few extra days”, as he had suggested in his leadership campaign, in order for the House of Commons to agree the terms of the UK’s departure.
Asked if a Brexit deal could be passed by MPs by 31 October, Mr Hunt told Sky News’ Kay Burley@Breakfast show: “It would be very, very challenging, I don’t want to say it’s going to be easy, but I think it’s not impossible.
“If we get a deal, people will heave a sigh of relief.
“And, frankly, if we need a few extra days beyond 31 October, I don’t think the 52% who voted Leave are going to mind provided we are properly on our way.”
Reflecting on his defeated leadership campaign, Mr Hunt said: “Of course, in some ways, it’s frustrating not to be close to the action now, but – I think like everyone – I’m really just hoping upon hope that Boris now succeeds.
“Everyone is just fed up with Brexit, they want it sorted.”
He also described Mr Johnson’s chief adviser, Dominic Cummings, as a “terrier” and someone who is “very, very determined to get the job done and has a particular set of qualities to bring, but is going to break a lot of china along the way”.
“If, in the end, he succeeds in getting us out of the EU with a deal – and this is now looking more possible than anyone might have thought – if he succeeds then people will say it was a very inspired appointment,” Mr Hunt added.
Ex-justice secretary David Gauke also raised an obstacle to Mr Johnson’s hopes of delivering Brexit by 31 October, as he suggested he and other former Conservative MPs could support a delay to the UK’s departure from the EU if necessary Brexit legislation looks unlikely to be passed by the end of the month.
Mr Gauke told Kay Burley@Breakfast: “If he [Mr Johnson the prime minister] has got a deal that he’s brought back, I would be supportive of that.
“There is just one point I would want to make – I wouldn’t want us to be in a position where we vote for a deal on Saturday and then something goes wrong in the next 12 days, and then we crash out without a deal on 31 October.”
Downing Street revealed a cabinet meeting due to be held today has been moved to Wednesday in order to allow ministers to receive a more detailed update on Brexit negotiations.