A third vote on the prime minister’s withdrawal agreement would come after MPs voted this week in support of a delay to 30 June.
Serial Tory rebel and Brexit-backer, Daniel Kawczynski, is the latest backbench MP to swing behind May’s plan in a bid to head off an extension.
But so far the number of Tories publicly switching positions has amounted to a trickle rather than the flood the PM needs to overturn the 149-vote defeat for the deal she suffered on Tuesday.
Kawczynski, the MP for Shrewsbury and Atcham, acknowledged that the deal was now the “only game in town”.
“Do we continue to obstruct and risk no Brexit? I doubt I can take that risk,” he said after talks with local Tories, farmers and businesses.
His comments came after former cabinet minister Esther McVey, who resigned over the Brexit deal, suggested she and other MPs could now back it, even though it was “rubbish”.
And North Wiltshire MP James Gray appealed to fellow members of the Brexiteer European Research Group (ERG) to get the “obnoxious” deal over the line because it was “the only way we can achieve anything which even vaguely resembles the Brexit that 17.4 million people voted for”.
But other ERG figures played down the prospect of large numbers swinging behind the deal when it is brought back for a vote.
Meanwhile, talks continued with the DUP, but the party stressed that the presence of Chancellor Philip Hammond at a meeting on Friday did not mean that money was an issue.
“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,” a spokesman said.
“Contrary to some reports we are not discussing cash.
“There are still issues to be addressed in our discussions.”
Labour’s John McDonnell indicated that MPs would “move heaven and Earth” to block a no-deal Brexit and continued to suggest the party could back a call to put a deal to a public vote.
He said: “We are working with Peter Kyle and Phil Wilson, they have their amendment, which was about going back to the people with whatever was agreed in parliament, so we’ve said we would support that if it comes back, and it may well be this week but it will be down to the tactics they want to pursue, because they will only push that when they think they’ve got a realistic prospect of winning.”
The prospect of the UK leaving the European Union on March 29 has receded after MPs authorised May to seek an extension to the Article 50 Brexit process.
Latvian foreign minister Edgars Rinkevics suggested a delay of up to two years could be required if MPs continue to reject the Brexit deal.
“Number one priority would be the deal that is reached is passed,” he told BBC Radio 4’s Today.
“If it is not the case what we need is clear vision from the UK government how much time the UK needs to come up with new proposals, new ideas how we proceed. In that case it’s not a couple of months, I believe then we are talking about maybe one or two years.”
European Commission vice-president Frans Timmermans indicated that any extension to Article 50 could be a two-stage process, initially limited to a few weeks unless May could set out what she wanted to achieve with the extra time.
He told Germany’s Funke newspaper “as long as this isn’t clear, Brexit can only be delayed for a few weeks, solely to avoid a chaotic withdrawal” on March 29.
“During this time, the British must tell us what they want: new elections? A new referendum? Only after that can we talk about a several-month extension,” he added.
Documents circulating among EU ambassadors make clear the bloc would terminate the UK’s membership on July 1 if it has not taken part in European Parliament elections.
The draft paper obtained by the Financial Times said Britain has to take part in the May 23-26 votes if it wants an extension of more than three months.
The EU guidance echoes the briefing provided to MPs at Westminster before Thursday’s vote, which said “if the UK were to seek an extension beyond July 1, and hence remain a member state beyond that point, it would need to participate in the EP elections”.
The government document stated that decisions needed to be made on the election by April 12, when returning officers must publish notice of the poll.
Some campaigners have called for a so-called People’s Vote referendum in which remaining in the EU is an option for voters.