Boris Johnson will make a final bid on Tuesday to force Brexit through by the 31 October “do or die” deadline, amid growing signs he will make a renewed push for a general election whether his deal passes or not.

Johnson has already requested a delay to Brexit, by sending the letter to Brussels required by the backbench Benn act after MPs declined to support his deal on Saturday – something he said he would rather be “dead in a ditch” than do.

But if the government can force its Brexit bill through parliament in time, the UK could in theory still leave the EU by next Thursday’s deadline.

The prime minister will ask MPs to back him in two crucial votes on Tuesday – on the withdrawal agreement bill, enshrining the deal he struck in Brussels last week, and on his plan to ram it through the House of Commons by the end of Thursday.

Johnson will tell MPs: “We have negotiated a new deal so that we can leave without disruption and provide a framework for a new relationship based on free trade and friendly cooperation. We are leaving the European Union but we will always be European”.

Johnson’s plan to hold a “meaningful vote” on his deal on Monday was blocked by the Speaker, John Bercow, who said it would be “repetitive and disorderly” to go over the same ground as Saturday’s vote.

With the backing of some Labour rebels and the Tories who backed Oliver Letwin’s amendment at the weekend, Johnson is expected to win the vote on his bill known as the second reading, signalling MPs’ approval for it to proceed in principle.

But Downing Street is braced for potential defeat on the so-called programme motion setting out the timetable, as it suspects some pro-deal Labour MPs and a few Conservatives may not support plans to rush it through the Commons within days.

Veteran Conservative Ken Clarke said: ““Unless you are prepared to contemplate more expansive debate, there is not the slightest possibility of considering the deal that has been obtained within the time available.”

The independent unionist MP Sylvia Hermon, who voted for Theresa May’s Brexit deal three times, said: “I would very much like the prime minister to come to Northern Ireland to explain in detail to the people why they only deserve three days’ consideration of the major changes to them and how this bill will affect their futures.”

The DUP’s chief whip, Jeffrey Donaldson, said: “I have to say to the leader of the house quite frankly that what he’s proposing in terms of proper scrutiny of this bill does not do justice to what the constituents that I represent need.”

If the programme motion falls, the government has little chance of “getting Brexit done”, as Johnson calls it, by 31 October.

If the bill continues its passage, groups of MPs are likely to try to amend the legislation – with Labour hoping to push for a customs union and for a second referendum to be attached.

Johnson has repeatedly insisted that he could not live with a customs union, as have several key cabinet ministers including Dominic Raab and Priti Patel. If such an amendment passed, he would face the choice of accepting it or making a fresh bid to call a general election.

One Conservative adviser said pro-Brexit cabinet ministers and Tory backbenchers would never be able to live with a customs union attached to the bill, so it was “not going to happen”.

The aide said this scenario would probably lead to renewed push for an election, with Conservative party headquarters still preparing for a pre-Christmas poll – regardless of whether the Brexit bill passes or not.

He also suggested that, with an election on the way, Johnson could part ways with Dominic Cummings, his controversial chief adviser, who had only ever planned to stay until Brexit was done and is due to have a major operation.

“Boris created the monster, so Boris could slay it,” the aide said, arguing that it could be an olive branch to former Tories who lost the whip and part of his pivot to a more centrist position on domestic issues.

Johnson has struck a notably more emollient tone in recent days, stressing his “love” of Europe and dialling down his criticism of the “surrender act”.

Another senior Conservative suggested Johnson’s team believed they were in a strong position, even if he broke his promise of achieving Brexit by 31 October.

“In any of the scenarios now, we’re probably quite well-placed,” he said. He added that the passing of the Letwin amendment on Saturday, withholding support from Johnson’s deal until the legislation is through parliament, would help Johnson to blame troublemaking MPs for the delay. “Letwin’s given us quite a lot of cover on this,” he said.

The 110-page withdrawal agreement bill was published on Monday evening. It confirms that MPs will have the opportunity to vote on what the government’s mandate should be for the next phase of negotiations.

And, as the government announced on Friday, ministers will have to seek the support of parliament when they depart from EU standards on workers’ rights.

The legislation may alarm some Eurosceptics by confirming - as Theresa May conceded back in 2017 - that EU law will continue to hold sway during the transition period. The transition is due to end in December 2020, but could be extended by two years with parliament’s approval.

Some Conservative MPs, including the former chancellor Philip Hammond, are seeking reassurances that the government will request such an extension if no trade deal has been agreed in time.

MPs’ concerns about the risks of rushing through the bill were underlined on Monday when the chancellor, Sajid Javid, conceded to MPs on the Treasury select committee that he had no plans to carry out a detailed economic assessment of the deal, which he claimed was “self-evidently in our economic interest”.

The shadow chancellor, John McDonnell, accused Javid of “flying blind on a massive decision on the future of the economy”.

The government’s claims that the Brexit bill could be properly scrutinised within three days was further undermined when Steve Barclay, the Brexit secretary, blundered over the implications of the bill for Northern Ireland, suggesting even he was not on top of the detail.

In a Lords EU committee, he initially claimed that Northern Ireland businesses would not have to fill out customs declarations to send goods to the rest of the UK. But after correction from the Treasury, he said: “The exit summary declarations will be required.”

The admission provoked fury from the DUP, with one of the party’s 10 MPs, Gavin Robinson, demanding: “Is it the case that Northern Ireland goods will require customs declarations to enter what is supposed to be unfettered access to the rest of their own country?”

Conservative whips are seeking to warn MPs in their party that voting against the programme motion risks scuppering the bill. The leader of the House of Commons, Jacob Rees-Mogg, said: “People who don’t vote for the programme motion will be voting not to have Brexit on 31 October.”