Boris Johnson will set out details of his "final" negotiating offer to the EU on Wednesday in pursuit of a "fair and reasonable" Brexit compromise.
The prime minister will address the Tory conference before submitting new proposals, intended to form the legal text of a new Brexit deal, to Brussels.
Only by leaving the EU on 31 October can the UK "move on", he will argue.
The public will no longer be "taken for fools" by those who want to delay or block the process, he will claim.
On the eve of his speech, Mr Johnson told a conference fringe meeting in Manchester, hosted by the DUP, that he hoped to reach a deal with the EU over the course of "the next few days".
The government has insisted it will not negotiate a further delay beyond the Halloween deadline, saying this would be unnecessary and costly for the UK.
However, under the terms of a law passed by Parliament last month, the PM faces having to request another extension unless MPs back the terms of withdrawal by 19 October - two days after a summit of European leaders.
On Tuesday, Mr Johnson dismissed leaked reports that customs posts could be set up on either side of the border between Northern Ireland and the Republic of Ireland.
He said suggestions the UK wanted "clearance zones" for goods as part of a package of alternative arrangements to replace the Irish backstop were wide of the mark.
While he conceded some customs checks would be needed as the UK leaves the EU's customs union and single market, he said technology could keep them to an "absolute minimum".
The BBC's Europe editor Katya Adler said the mood in Brussels was "not optimistic".
She said EU leaders feared the prime minister's proposed alternative to the Irish backstop could mean the bloc abandoning its red lines - something member states were not willing to do at the moment.
Irish Fine Gael senator Neale Richmond told BBC Radio 4's Today programme that the PM's plans were a "big move" from the withdrawal agreement made by Theresa May.
Mr Richmond said, under the plan, Northern Ireland would leave the customs union and "come out of the single market in all areas, apart from agri-food products and industrial products, and indeed it only stays in those areas for four years".
This, he added, would required "additional checks" on the island of Ireland - something he described as "extremely disappointing".
In his keynote speech to the party faithful in Manchester - his first as prime minister - Mr Johnson will unveil what he hopes will be the basis of a compromise that can win the backing of MPs.
And BBC assistant political editor Norman Smith said it was particularly important Mr Johnson secured the support of the Democratic Unionist Party's 10 MPs.
He said: "I think it is very clear this deal is not going to fly unless Boris Johnson can bring the DUP along with him... one way or another he has to make sure they're on board."
Speaking in Manchester, Mr Johnson will suggest voters are "desperate" for the country to focus on other priorities and will contrast his determination to leave on 31 October with the "years of uncertainty" that he says would result from a Labour government promising another referendum.
"What people want, what Leavers want, what Remainers want, what the whole world wants - is to move on," he is expected to say.
"I am afraid that after three-and-a-half years people are beginning to feel that they are being taken for fools.
"They are beginning to suspect that there are forces in this country that simply don't want Brexit delivered at all.
"And if they turn out to be right in that suspicion then I believe there will be grave consequences for trust in democracy.
"Let's get Brexit done on October 31 so in 2020 our country can move on."
'Respect the vote'
The BBC's political editor Laura Kuenssberg said the decision in the next few days would not be about whether there is a deal or not, but whether "the two sides reckon it's worth sitting down to talk properly at all".
'We will not be dragged out of the single market'
Diane Abbott to stand in for Corbyn at PMQs
Ahead of Wednesday's speech, No 10 insisted if the EU did not engage with the UK's offer there would be no further negotiations until after it had left on 31 October.
"The government is either going to be negotiating a new deal or working on no deal - nobody will work on delay," a senior No 10 official said.
Mr Johnson's conference speech is set to clash with Prime Minister's Questions, which is taking place at 12.00 BST.
Normally the Commons goes into recess for the Tory conference, but MPs voted against this amid the bitter fallout from the government's unlawful prorogation of Parliament.
Foreign Secretary Dominic Raab will deputise for the prime minister, facing the shadow home secretary Diane Abbott over the despatch box.