With just over a month until Britain is due to leave the bloc on March 29, Prime Minister Theresa May is seeking changes to her exit deal in order to break an impasse in parliament.

Labour’s decision could damage her hopes of winning support for a revised deal in a vote she has promised by March 12, by attracting those who would have backed her agreement in order to avoid a no-deal exit but who would prefer a second referendum.

Parliament is due to debate and vote on Wednesday on the next steps in Britain’s tortuous departure from the EU, and lawmakers are set to offer proposals, or amendments, which could include demanding the exit deal is put to a public vote.

Labour said it would put forward an amendment calling on the government to adopt its Brexit proposals, which include a permanent customs union with the EU and close alignment with the bloc’s single market.

“If Parliament rejects our plan, then Labour will deliver on the promise we made at our annual conference and support a public vote,” Labour’s Brexit spokesman Keir Starmer said.

Parliament is not expected to back Labour’s Brexit plan and it remains unclear whether there is a majority in parliament in favour of holding a second referendum.

“We’re in a very volatile situation. We are in the middle of a political crisis and a constitutional crisis... It’s difficult to say at any one point what feelings are going to be two or three weeks down the line,” a Labour spokesman told reporters.

Labour leader Jeremy Corbyn has been under pressure for some time to support a second referendum. Last week, eight referendum-supporting lawmakers quit the party, in part owing to frustration over his failure to back another vote.

The prospect of holding a second vote poses a dilemma for Corbyn: while many of the party’s members and supporters fervently back a so-called People’s Vote, others simply want Britain to leave the EU as soon as possible.

Labour said it would support a bid by its lawmaker Yvette Cooper to give parliament the legal power to force May to delay Brexit by seeking an extension to the Article 50 negotiating period.

“We are committed to also putting forward or supporting an amendment in favour of a public vote to prevent a damaging Tory (Conservative) Brexit being forced on the country,” Corbyn was due to tell a meeting of his lawmakers on Monday, his office said.

“One way or another, we will do everything in our power to prevent no deal.”

Brandon Lewis, Chairman of May’s Conservatives, said another popular vote would “take us back to square one” and Labour had gone back on its promise to respect the 2016 referendum result. That went 52-48 percent in favour of leaving the EU.

The amendment on a public vote may not come at this week’s vote in parliament however. The Labour spokesman said the wording and timing of the amendment was still to be decided.

A proposal by Labour lawmakers Peter Kyle and Phil Wilson that May’s deal be put to the public in another referendum will not be put forward for a vote in parliament until May brings her agreement back for approval.

“There’s no turning back for Jeremy now,” Kyle said.

Labour lawmakers at the meeting on Monday were split in their reactions.

“I still have deep reservations about the idea of having another referendum. I think it’s going to be deeply divisive,” lawmaker Stephen Kinnock said.

Labour foreign affairs spokeswoman Emily Thornberry told ITV a second referendum should present a choice between May’s deal and remaining in the EU, but the Labour spokesman directly contradicted her, saying that would be an unacceptable choice.

The Remain Labour campaign group, which wants to stop Brexit, said the announcement was “a significant step forward”.

“A second referendum was only ever possible with the votes of Labour Members of Parliament and we are now on the verge of making this happen,” founder Andrew Lewin said in a statement.

“We are not complacent, but we are closer tonight to a People’s Vote than we have ever been.”