The former work and pensions secretary Esther McVey, who resigned in protest against the prime minister’s Brexit deal, has confirmed she now plans to vote for it this week, raising hopes that it could yet be approved.

Theresa May’s deal was rejected by a majority of 149 last week, but McVey said she would “hold her nose” and approve it, after a pair of votes in parliament last week that rejected a no-deal Brexit and called for a delay.

“The rules have all changed,” McVey said. “We all stood on a manifesto that no deal is better than a bad deal, and I still believe that Theresa May’s deal is a bad deal – but after the votes in the house last week, that isn’t the option facing us any more.

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“No deal has been removed; article 50 will be extended; so the choice before us is: this deal or no Brexit whatsoever – and to not have Brexit you go against the democratic vote of the people,” she told Sky’s Sophy Ridge on Sunday.

McVey’s change of heart, which she hinted at last week, came amid other signals that last week’s votes may have shifted the terrain in parliament.

A backbench rebel, Daniel Kawczynski, has publicly indicated he would now back the prime minister’s plan. Kawczynski, the MP for Shrewsbury and Atcham, acknowledged the prime minister’s deal was now the “only game in town”.

Another Brexiter, the MP for North Wiltshire, James Gray, appealed to fellow members of the Brexiter European Research Group to get the “obnoxious” deal over the line.

And Matthew Elliott, who was chief executive of the Vote Leave campaign, recommended supporting the deal. “If MPs vote down the withdrawal agreement for a third time this week, Brexit probably won’t happen,” he said. “But if MPs do allow the meaningful vote to pass, we will leave in a matter of weeks … We will be free from the political institutions of the EU by the summer.”

Facebook Twitter Pinterest Philip Hammond suggested it was physically impossible for Britain to leave the EU on 29 March. Photograph: Reuters

The chancellor, Philip Hammond, said there would not be another meaningful vote this week unless the prime minister believes she can win it.

“We will only bring the deal back if we are confident that enough of our colleagues, and the DUP, are prepared to support it, so that we can get it through parliament. We’re not going to keep presenting it if we haven’t moved the dial,” he said.

He suggested it was physically impossible for Britain to leave the EU on 29 March, because there is not enough time for all the relevant legislation to be passed – but it could happen in April or May if the deal is agreed this week.

Hammond also confirmed that talks were continuing with the Democratic Unionist party. He said the main emphasis was on reassuring them that new barriers would not be allowed to develop between Northern Ireland and Great Britain, if the backstop was invoked.

“I regard it as crucially important that we do not allow differences to grow up between Northern Ireland and Great Britain, and we’re looking for ways in which the government can reassure Northern Irish politicians about our clear intention to make sure that there are no such differences as we go forward, if the backstop had to come into force,” he said.

Asked if extra funding for Northern Ireland could be involved, as it was in clinching the DUP’s support for May’s minority government two years ago, Hammond said: “We are coming up to a spending review, and we will have to look at all budgets, including devolved block-grant budgets, in that spending review: of course we will.”

The prime minister used an article in the Sunday Telegraph to warn MPs that if they failed to back her Brexit deal at the third time of asking then Brussels might insist on a lengthy delay, potentially scuppering chances of leaving the EU altogether.

She said it would be a “potent symbol of parliament’s collective political failure” if a delay to Brexit meant the UK was forced to take part in the European elections in May, almost three years after voting to leave.

She warned that if MPs did not back her deal before Thursday’s European council summit “we will not leave the EU for many months, if ever”.

May acknowledged that even if her deal were passed before the summit of EU leaders, the government would need a “short technical extension” beyond the scheduled 29 March Brexit date.

“That is not an ideal outcome – we could and should have been leaving the EU on March 29,” she said.

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“But it is something the British people would accept if it led swiftly to delivering Brexit. The alternative if parliament cannot agree the deal by that time is much worse.”

In a message aimed at MPs seeking rival versions of Brexit, she said: “If the proposal were to go back to square one and negotiate a new deal, that would mean a much longer extension – almost certainly requiring the United Kingdom to participate in the European parliament elections in May.

“The idea of the British people going to the polls to elect MEPs three years after voting to leave the EU hardly bears thinking about. There could be no more potent symbol of parliament’s collective political failure.”

McVey hinted at some of the demands Brexiters may make in return for their backing this week, saying the prime minister should replace the Brexit negotiating team – and may need to think about her own position.

“She will have to decide what she is going to do,” McVey said, but attacked May for voting for a Brexit extension. “She and the team walked through the [voting] lobby extending that date, so she’s made life very difficult for herself. That’s what now she’s got to look at – has she got discipline in the government?”

The former Brexit secretary David Davis said May’s deal was “capable of rescue” if the negotiating strategy were changed and experienced trade negotiators brought in to work with the EU. Writing in the Sunday Times, he added: “Judging by last week the alternative would be a cascade of chaos, eventually ending in a remainer attempt, first to delay Brexit by a long time and then reverse it.”

Many Brexiters are watching closely to see if the Democratic Unionist party can be won over in the days ahead. Talks have continued after a series of meetings on Friday involving the DUP’s Nigel Dodds and several key ministers including the chancellor.

A DUP spokesman said: “We are in discussions with the government to ensure Northern Ireland is not separated out from the rest of the United Kingdom as we leave the European Union. Contrary to some reports we are not discussing cash. There are still issues to be addressed in our discussions.”