Theresa May has urged MPs to back her Brexit deal "for the country's sake" as Tuesday's Commons vote looms closer.
She warned of "paralysis in Parliament" if the deal is rejected and said trust in politics would suffer "catastrophic harm" if the UK did not leave the EU.
The PM welcomed new EU assurances over the impact of the deal on Northern Ireland, saying they had "legal force".
The EU said it didn't want to use the "backstop" but, if it did, it would be for "the shortest possible period".
The "backstop" is the fallback plan to avoid any return to physical Northern Ireland border checks.
In a letter to Mrs May, the EU said commitments to look at alternatives to the customs arrangement and to fast-track talks on future relations had "legal value" and would be treated "in the most solemn manner".
Speaking in Stoke, Mrs May said "they make absolutely clear that the backstop is not a threat nor a trap".
But critics said they fell way short of the firm end date or the unilateral right to withdraw they wanted, with the Democratic Unionist Party saying "nothing has changed" and accusing the prime minister of "foolish talk".
Assistant whip Gareth Johnson became the latest member of the government to quit his job over the deal, saying in his resignation letter to the PM that it would be "detrimental to our nation's interests".
He added: "The time has come to place my loyalty to my country above my loyalty to the government."
Mrs May's speech comes amid reports MPs plan to take control of Brexit if her deal is defeated.
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.
Speaking to factory workers, Mrs May said she now believed MPs blocking Brexit was more likely than a no-deal scenario.
"As we have seen over the last few weeks, there are some in Westminster who would wish to delay or even stop Brexit and who will use every device available to them to do so...
"While no deal remains a serious risk, having observed events over the last seven days, it is now my judgment that the more likely outcome is a paralysis in Parliament that risks there being no Brexit.
Failing to honour the 2016 Brexit referendum vote would do "catastrophic harm" to the democratic process, she warned.
"Imagine if an anti-devolution House of Commons had said to the people of Scotland or Wales that despite voting in favour of a devolved legislature, Parliament knew better and would overrule them.
"Or else force them to vote again. What if we found ourselves in a situation where Parliament tried to take the UK out of the EU in opposition to a remain vote?
But Mrs May had been accused of "hypocrisy" by Welsh opposition politicians after excerpts of the speech released to the media in advance suggested she would cite the example of the Welsh devolution referendum in 1997, when people voted by a margin of 0.3% to create the Welsh Assembly, and argue that the result had been "accepted by both sides".
When she actually delivered the speech, the PM said the result had been "accepted by Parliament".
Mrs May voted against the establishment of the Welsh Assembly after that referendum - while the 2005 Conservative manifesto pledged to offer the Welsh people a "referendum on whether to keep the Assembly in its current form, increase its powers or abolish it".
What happens next?
Here is what is likely to happen:
Monday - Day four of MPs' Brexit debate, with the PM set to make a statement to the Commons setting out reassurances from the EU over the Irish backstop
Tuesday - Day five of debate followed by "meaningful vote" on the PM's deal. MPs will also get to vote on amendments that could reshape the deal. If the deal is rejected Theresa May will get three working days to come up with a "plan B"
Wednesday - Mrs May is likely to head to Brussels to try to get further concessions from the EU
Monday 21 January - Expected Commons vote on "Plan B"
The UK will leave the EU on Friday, 29 March, unless MPs vote to delay or cancel Brexit.
What are others saying?
Liberal Democrat leader Sir Vince Cable - who opposes Brexit - said: "The increasingly desperate language from the prime minister more than suggests a great deal of panic.
"But she cannot be allowed to pull the wool over the public's eyes. A chaotic no-deal Brexit is a choice and it is in the gift of the government to prevent it."
He argued that the best way forward was to have another referendum, including the option to remain in the EU.
Speaking to BBC Breakfast, Labour MP Chuka Umunna, who is also campaigning for another referendum, said Mrs May's deal would do "great harm to our economy".
But Labour's John Mann told Sky News there had to be a negotiated exit from the EU and "at some stage" he would back a deal, adding "it may well be tomorrow".
What has the UK been offered on Northern Ireland?
The so-called Irish backstop will see the UK and EU share a single customs territory until they settle their future relationship or come up with another solution to stop a hard border.
Many Tory MPs, as well as the Democratic Unionists are adamantly opposed to it.
The EU has given fresh written assurances about how the backstop might be triggered and how long it would last, assurances which it says have "legal value".
The key points, in a letter from Donald Tusk and Jean-Claude Juncker, to the PM are:
The backstop will not affect or supersede the provisions of the 1998 Good Friday Agreement
The backstop will not extend regulatory alignment with EU law in Northern Ireland beyond what is strictly necessary to avoid a hard border
Alternatives to the backstop such as "facilitative arrangements or technologies", will be looked at with progress considered every six months after the UK's departure
Any alternative arrangements would not be "required to replicate" the backstop "provided the underlying objectives continue to be met"
"Were the backstop to enter into force in whole or in part, it is intended to apply only temporarily, unless and until it is superseded by a subsequent agreement," they said.
"The Commission is committed to providing the necessary political impetus and resources to help achieving the objective of making this period as short as possible," it said.
But Conservative former work and pensions secretary Esther McVey said "warm words" from the EU were insufficient.
"The default position is going into the backstop," she said. "If the UK and the EU don't want it, let's take it out."
And the DUP's deputy leader Nigel Dodds said the EU was "not prepared" to do what was required to get the deal over the line.
"Despite a letter of supposed reassurance from the European Union, there are no 'legally binding assurances' as the prime minister talked about in December. In fact, there is nothing new," he said.
"Instead of meaningless letters, the prime minister should now ask for and deliver changes to the Withdrawal Agreement."
What about reports of MPs planning to take over Brexit?
The UK will leave the EU on 29 March unless there is a new act of Parliament preventing that.
Because the government controls the timetable for Commons business, it was assumed that this would not be possible.
But three senior Conservative backbenchers are to publish a bill on Monday night that would allow MPs to frame a "compromise" Brexit deal if Theresa May fails to come up with a plan B, Tory Nick Boles has revealed.
Mr Boles said he, Sir Oliver Letwin and Nicky Morgan were behind the "European Union Withdrawal Number 2 Bill", which would see the Liaison Committee - made up of the chairmen and chairwomen of all the Commons select committees - take a key role if the PM's Withdrawal Agreement is rejected by Parliament.
Mr Boles said all three planned to vote for the PM's deal, but would act if it failed.
He told BBC Radio 4's Today programme: "This bill would do the following: it would give the Government three more weeks to get a compromise deal, a plan B, through Parliament so that we are leaving the EU on time on March 29 with a deal.
"If that failed, it would... give the Liaison Committee the responsibility to try and come up with its own compromise deal, which would have to go back to the House for a vote."
Downing Street has said it is "extremely concerned" about the plot, which it says could potentially overturn centuries of Parliamentary precedent.
Are more Tory backbenchers coming round to the deal?
Four Conservative Brexiteer MPs who have been critics of the withdrawal agreement have now said they will support the government in the vote on Tuesday.
Sir Geoffrey Clifton-Brown, MP for the Cotswolds, said he still had "deep misgivings" about many aspects of Mrs May's deal.
But he said: "The events of last week have clearly demonstrated that the Speaker and MPs who wish to remain in the EU will stop at nothing to prevent that happening."
Former Public Accounts Committee chairman Sir Edward Leigh said Brexit-supporting MPs were "playing with fire" if they voted down the deal.
Former ministers Andrew Selous and Andrew Murrison and Caroline Johnson, MP for Sleaford and North Hykeham, also said they were backing the government despite reservations.
What are the chances of another referendum on leaving the EU?
A cross-party group of anti-Brexit politicians have published proposed legislation to bring about a second referendum on leaving the EU.
The draft Bill recommends that the public be asked whether they want to remain in the EU or leave under the prime minister's deal.
The MPs behind the draft legislation point out that Article 50 - the two-year process by which an EU member leaves the bloc - would have to be extended in order for another poll to take place, meaning the UK would remain a member beyond 29 March.
The legislation could be introduced through the House of Lords under plans being considered by the group.