A crunch vote in which MPs could force Theresa May’s hand on Brexit is set to be delayed until the end of the month or even later, it has emerged, as the prime minister travelled to Dublin for urgent talks with fewer than 50 days left to departure from the EU.

Under the timetable agreed by the government, May must either present a revised Brexit deal to the Commons on Thursday, which appears unlikely to happen, or else table a motion to which MPs can add amendments.

In a similar process just over a week ago, the Commons supported May’s attempt to renegotiate the Irish backstop but voted down amendments tabled by cross-party alliances of Brexit-sceptic MPs that would have extended article 50 and given parliament more control.

It had been expected the MPs would try again on Thursday if May did not return with a deal. But sources close to the group, led by the Tory MP Nick Boles and Labour’s Yvette Cooper, said it seemed likely that the prime minister would be given more time to discuss a Labour Brexit proposal and hold more talks with Brussels.

“The Tory MPs are keen to give the PM a chance to follow up on the cross-party talks, and negotiations with the EU,” the source said. A bill laying out how MPs could seek to avoid a no-deal departure may nonetheless be published next week, they said.

“There’s a definite sense that lots of Tories are worried about no deal, but they don’t want to look like they are trying to obstruct her negotiations,” the source said. “There is very definitely a majority in parliament against no deal, but it’s a question of how to proceed and when.”

The Liberal Democrat MP Norman Lamb, who supported the last Cooper-Boles amendment, told the Guardian: “Our position is that the ball is in the PM’s court. What we do depends on what the PM does.”

Any further delay would be contingent on May promising a future date for either a vote on her deal or another amendable motion, he said, adding: “Parliament has to have its say.”

It sets the scene for an increasingly tense couple of weeks in which May will attempt to stitch together a Brexit plan that can get a parliamentary majority while the EU and backbenchers watch the clock tick down towards 29 March.

After a bruising set of talks in Brussels on Thursday in which the European council president, Donald Tusk, mentioned Jeremy Corbyn’s proposals as a way of breaking the impasse, May was to meet the taoiseach, Leo Varadkar, for a dinner in Dublin on Friday.

The talks were intended to build on discussions May had in Northern Ireland and Brussels this week, her spokeswoman said. “She’ll be emphasising what we are looking for: seeking the legally binding changes to the withdrawal agreement that parliament said it needs to approve the deal.”

Earlier on Friday the attorney general, Geoffrey Cox, met his Irish counterpart, Séamus Woulfe, for talks on the backstop, the insurance policy intended to prevent a hard border on the island of Ireland if no permanent agreement can be reached.

May and Cox are pushing for changes to the backstop such as a time limit or a unilateral exit mechanism for the UK, a key demand of the DUP and many Conservative backbenchers, but the chances of any progress seem slight.

Speaking earlier in Belfast, where he met Northern Irish parties, Varadkar said that while the meal with May was an opportunity to “share perspectives” on Brexit, actual negotiations “can only be between the European Union and the United Kingdom”.

“There is much more that unites us than divides us and time is running short, and we need to get to an agreement really as soon as possible,” he said.

In an interview shown on RTE, the Irish state broadcaster, on Friday night, Varadkar said he thought a deal could be done, but he was unsure if it would happen before the UK leaves the EU. “I think that on balance we will secure a deal – whether it will be by the end of March or after an extension, I can’t say,” he said.

May has yet to formally respond to Corbyn’s letter on Wednesday in which he said Labour would support her Brexit deal if she makes five legally binding commitments, including joining a customs union.

The Labour leader faces disquiet from some of his MPs over the move, which some have interpreted as a shift away from the possibility of pushing for a second referendum.