LONDON -- British Prime Minister Theresa May is making a final push to save her European Union withdrawal deal after a promise to step down failed to win over lawmakers from Northern Ireland.

May pledged Wednesday night that she would quit if the deal were approved, in hopes of blunting opposition from lawmakers who have criticized her leadership. Some prominent opponents, including former Foreign Secretary Boris Johnson, quickly said they would to back the agreement, but Northern Ireland's Democratic Unionist Party said it remained opposed because of concern that it treats the region differently from other parts of the U.K.

The prime minister's announcement came as lawmakers rejected eight alternatives to her deal after an unprecedented move to wrest control of the parliamentary agenda from the government in an attempt to find a plan that could break the Brexit deadlock. While the architect of the so-called indicative votes said there would be a second round of voting on Monday, even he said Wednesday's events meant a damaging no-deal Brexit was becoming more likely.

"I think that at some point or other we either have to get her deal across the line or accept that we have to find an alternative if we want to avoid no deal on the 12th, which I think at the moment is the most likely thing to happen," Conservative Party lawmaker Oliver Letwin told the BBC.

The EU last week extended the Brexit deadline for two weeks, saying Britain would leave the bloc with no deal on April 12 if it doesn't come up with a plan to break the deadlock by that date. If Parliament approves May's deal by Friday, the deadline will be extended until May 22 so there is time to pass implementing legislation.

May has been under mounting pressure to quit as lawmakers accuse her of failing to work with other parties to find a Brexit plan that could win support in Parliament and then negotiating a bad divorce deal that is criticized both for failing to protect the economy and for leaving Britain too closely tied to the EU.

Brexit Secretary Stephen Barclay said the outcome of Letwin's so-called indicatives votes showed May's deal is still "the best option" for avoiding a no-deal departure as he appealed for lawmakers to support the agreement.

But supporters of Letwin's effort to find a way forward said they weren't daunted by Thursday's results because the plan was always to hold a second round of voting on Monday after the first ballot eliminated ideas that had no chance of commanding a majority.

The idea of a customs union with the EU came closest to winning a majority, with 264 lawmakers voting for it and 272 voting against. The most popular option was the idea of holding a second referendum on any deal approved by Parliament, which was backed by 268 lawmakers, but opposed by 295.

"The reason there's all this fuss about how terrible it was is because the people who want no deal want it to look as if nothing else is happening and everything has failed so we have to go their way," said Labour Party lawmaker Margaret Beckett, who sponsored the second referendum proposal.