A backbench plan to ward off a no-deal Brexit by extending article 50 is in the balance amid concerns from Labour MPs in leave-voting seats, who fear it could be seen as an attempt to frustrate Britain’s departure from the EU.

It appears likely that the Labour front bench will support the amendment to the government’s Brexit deal tabled by Yvette Cooper. Cooper’s amendment has already won the backing of more than 70 cross-party MPs, among them a number of Conservatives.

This month an earlier Cooper amendment to restrict the chances of no deal was passed with the support of 20 Conservatives, However, while just three Labour MPs went against the party line in that vote, there is speculation that more could rebel on Tuesday.

The new amendment, which seems likely to be among those selected for a vote, would guarantee parliamentary time for a private members’ bill drafted by Cooper that would extend article 50 to the end of 2019 if Theresa May failed to secure a deal by late February.

Some Labour MPs representing seats that voted leave in the 2016 referendum have warned that the plan could appear to be endlessly extending the Brexit process for no reason.

Labour sources said some MPs – over and above the half a dozen or so who have voted with the government on May’s Brexit plan – had come to the whips’ office to express reservations about the Cooper amendment.

Some are concerned that it could be used to pave the way for a second referendum, and they are expected to study the amendment over the weekend before coming to a final position.

Lisa Nandy, who represents Wigan, where 64% voted leave in 2016, said she would back an extension of article 50 if there was a clear justification, such as the idea of a citizens’ assembly, which she supports, but was otherwise wary.

Nandy said: “Without a clear reason, people will understandably think we’re just kicking this into the long grass and the ongoing chaos is making it impossible for local businesses.”

Another obstacle would be what to do with European elections due to take place in late May if Brexit were delayed beyond then, Nandy said.

“I haven’t yet heard any convincing explanation that would avoid us then having to campaign to re-elect MEPs to a parliament we were supposed to have left months earlier. That just strikes me as completely unsustainable,” she said. “So I haven’t dismissed the amendment out of hand, as avoiding no deal is clearly important, but there are serious problems with it as it currently stands.”

On Friday, Andrea Leadsom became the first leave-backing cabinet minister to acknowledge that the Brexit deadline could be extended beyond 29 March, though only briefly.

The leader of the Commons, who is in charge of guiding Brexit legislation through parliament, told BBC’s Newsnight that a short extension was feasible: “I am absolutely certain that if we needed a couple of extra weeks or something, then that would be feasible.”

The parallel issue of a possible second Brexit referendum remains the subject intense debate within Labour, with a senior ally of Jeremy Corbyn warning that it could badly affect the relationship between politicians and the public.

Ian Lavery, the MP for Wansbeck and Labour’s national campaigns coordinator, said that while the idea was still possible under party policy as a way to end an otherwise intractable Brexit impasse, he was worried about the consequences.

“We should be in no doubt that asking the voters to vote again on an issue they have already given an answer, until they come up with the right answer, risks serious damage to the relationship between many citizens and politicians at Westminster,” he wrote in an article for the Guardian.

Earlier in the week, a planned cross-party amendment for a “people’s vote” was dropped by its organisers, who said the lack of explicit Labour front-bench backing meant it was unlikely to pass.

However, the Commons order paper for Tuesday’s crucial series of votes on the next stages for Brexit now features three new amendments tabled by Labour MPs seeking the same.

On Saturday, campaigners from the People’s Vote campaign were promising to hold events in about 100 places across the UK to maintain the pressure for a second referendum.