Theresa May has told the BBC that MPs will have a choice between her proposed deal with the EU – or no deal at all.
In an interview with Panorama, she is also critical of plans by Brexiteers to resolve the Irish border issue.
But ex-foreign secretary Boris Johnson claims the government’s failure to resolve the border question has led to a “constitutional abomination”.
A BBC-commissioned survey indicates more people across the UK think the impact of Brexit will be negative.
Speaking to the BBC’s Nick Robinson, Mrs May says that if Parliament does not ratify the Chequers plan “I think that the alternative to that will be having no deal”.
But Mr Johnson’s column in Monday’s Daily Telegraph criticises her strategy to leave the EU.
He says Mrs May’s Chequers plan “would mean for the first time since 1066 our leaders were deliberately acquiescing in foreign rule”.
He describes a backstop for the Irish border as “an attempt to annex Northern Ireland” by Brussels in creating a border down the Irish Sea.
Mr Johnson says the prime minister’s solution to the Irish border question in the Chequers plan would mean the UK “must remain effectively in the customs union and large parts of the single market until Brussels says otherwise”.
by Chris Mason, political correspondent
The Prime Minister’s vision for Brexit has had bricks thrown at it at home, and in Brussels too. But her determination to stick with it – and sell it – continues; to the EU, to MPs, to Conservative activists and the wider public.
And there is, she says, a binary choice. Her deal or no deal.
Last week Conservative Brexiteers opposed to her plan set out their own ideas, including using technology to avoid checks at the Irish border. But, Mrs May argues, they are a non-starter.
But Boris Johnson claims the government’s failure to resolve the border question has led to a “constitutional abomination” that will lead to a “total write-off of Brexit.”
In her Panorama interview, Mrs May says there needs to be “friction-free movement of goods” with no customs or regulatory checks between the UK and EU on the island of Ireland, in order to avoid a hard border there.
Last week a group of Brexiteer Tory MPs said a hard border could be avoided by using “established” technology and “modifying” existing arrangements.
Mr Johnson refers to the suggestions by the European Research Group (ERG) in his column, saying that “extra checks done away from the border” would prevent the need for physical checks when vehicles move between Northern Ireland and the Irish Republic.
But Mrs May insists that any system of checks is “still a hard border”.
“You don’t solve the issue of no hard border by having a hard border 20km inside Ireland,” she says.
The Times has reported that the EU is “secretly preparing to accept a frictionless Irish border”.
It says the EU’s chief negotiator Michel Barnier is working on a new “protocol” text outlining a plan to use technology to minimise checks.
Mrs May has found herself embattled with some in her party, after about 50 members of the ERG openly discussed how and when they could force her to stand down as prime minister.
But Brexit-supporting Environment Secretary Michael Gove said the Chequers plan was the right one “for now”.
On Sunday he told Andrew Marr that a future prime minister could alter the relationship between the UK and the EU.
But he added: “The Chequers approach is the right one for now because we have got to make sure that we respect that vote and take advantage of the opportunities of being outside the European Union.”
With nearly six months to go until exit from the EU on 29 March 2019, a poll commissioned by BBC Radio 5 Live suggests that the UK remains split over whether Brexit will be positive for the UK.
According to a Comres survey, 50% of British adults feel the overall impact will be negative, whereas 41% think it will be positive.
When asked about the handling of Brexit negotiations, almost 79% of people polled thought that the government had handled them badly, and 63% thought the EU had handled them badly.
BBC Panorama, Inside No 10: Deal or No Deal? is on Monday 17 September at 20:30 BST on BBC One as part of a week of in-depth coverage across the BBC to mark Brexit: Six Months to Go.