By William Booth, Karla Adam, Washington Post–

British Prime Minister Theresa May told her Conservative Party lawmakers Wednesday that she was prepared to resign before the next round of Brexit negotiations, offering up her leadership post to convince hardliners to pass her unpopular plan to exit the European Union.

In other action, the House of Commons could not produce a majority for any of the eight different Brexit proposals put forth by members in a special, late-night session of “indicative votes,” that were designed to help find new ways to break the impasse.

The closest votes were for a soft Brexit based on a new customs union with the E.U., which lost by eight, and a call to stage a second Brexit referendum, which lost by 27.

So Brexit remains at a standstill — though May’s offer to quit if her Brext deal is eventually passed offered some hope she might eventually get the withdrawal through the House.

May offered no timetable for her departure. Some Tory lawmakers said a leadership election within the party could happen over the summer, with May leaving 10 Downing Street by the autumn. Other reports suggested a new leader could be in place by July. Swapping prime ministers within the party would not require a general election.

May’s announcement was made behind closed doors, at a meeting of backbench, rank-and-file Conservative Party members at the Palace of Westminster. There were no reporters in the room.

“I have heard very clearly the mood of the parliamentary party. I know there is a desire for a new approach, and new leadership, in the second phase of the Brexit negotiations, and I won’t stand in the way of that,” she told the Tory lawmakers, according to excerpts released by Downing Street.

“I am prepared to leave this job earlier than I intended in order to do what is right for our country and our party,” she said.

While May’s offer to step aside encouraged a number of Conservative rebels to say they now will support for her twice-defeated Brext deal, she still may not have enough votes for the deal to pass this divided Parliament.

It was also unclear if May’s promise to resign would be honored if lawmakers do not approve her exit deal.

Crashing out of the European Union without a deal, as well as a long delay, a general election or a second referendum all remain live options, as the chaos of Brexit continued.

The prime minister’s surprise announcement was seen as key to getting dozens of hardcore Brexiter lawmakers, including Boris Johnson and Jacob Rees-Mogg, to back her Brexit play.

Johnson suggested to colleagues he will now support May’s Brexit deal. Rees-Mogg, a Conservative lawmaker who is something of a power broker in these negotiations, said he would back May’s deal as long as Northern Ireland’s Democratic Unionists did. He tweeted that “half a loaf is better than no bread.”

But on Wednesday night, the DUP said it still could not back May’s Brexit, saying that the risk that Northern Ireland would be trapped by the arrangements made over how to keep the Irish border open was too great.

Without the DUP on board, May’s deal faces tough odds.

Critics were quick to note how vague May’s vow to step down was.

“If I were them, I’d want it in blood,” Margaret Beckett, a Labour Party politician, told the BBC. “I’ve lost track of how many times she’s promised she won’t lead them into the next election and suddenly it’s turned out that she might after all.”

May was also criticized for focusing on her party and its fractious nay-sayers.

“Theresa May’s pledge to Tory MPs to stand down if they vote for her deal shows once and for all that her chaotic Brexit negotiations have been about party management, not principles or the public interest,” tweeted opposition Labour Party leader Jeremy Corbyn. “A change of government can’t be a Tory stitch-up, the people must decide.”

The Conservative Party has a long history of leaders falling over Europe: David Cameron, Margaret Thatcher and John Major were all toppled in part because of issues relating to Britain’s relationship to the continent.

But many lawmakers — of all parties — believe May has made a shambles of the exit.

Her rightwing critics say May’s Brexit plan could leave the United Kingdom too closely tied to European rules and regulations, failing the test of “taking back control” from Brussels. Those who want a softer Brexit say May threw down too many red lines during negotiations.

May says the withdrawal agreement, negotiated with her European counterparts over the past two years, is the best possible deal and honors the results of the June 2016 referendum, which saw voters opt for Brexit by 52 percent to 48 percent.

With the news that she may be stepping down, the British chattering class quickly pivoted to speculation over who might replace her.

The top contenders, at least on Wednesday, included Johnson and the government ministers Michael Gove, Jeremy Hunt, David Lidington and Sajid Javid.

Although May dominated the headlines, Parliament had hoped it would be able to take control of the Brexit process on Wednesday, to find out on what kind of Brexit the fractious, quarreling, paralyzed lawmakers wanted.

Their answer was a mush.

There was neither clear majorities for a “soft” or “hard” exit from the European Union.

The Labour Party’s plan for an “alternative” Brexit also failed.

The votes were non-binding. There may be another round of such “indicative” votes next week.

The House of Commons has in the past three months said what it does not want. Lawmakers two times voted overwhelmingly against May’s Brexit deal. They also said they do not want Britain to leave the continental trading bloc without a deal.

May is still pressing lawmakers to support her Brexit deal in a third vote, which could take place later this week or early next.

The Brexit Secretary Stephen Barclay told the House that the voting demonstrated “there are no easy options here. There is no simple way forward.” He said the best deal on offer was the one May has negotiated and he urged them to reconsider.

“If we do not do that,” Barclay said, “then there are no guarantees about where this process will end.”

Things may be confusing on the Conservative benches, but they aren’t any clearer on the Labour ones, which has been trying to appease both the “remainers” and “leavers” in their party.

It did not go unnoticed at the massive on march Saturday — where an estimated 1 million took to the streets to demand a second referendum — that Labour sent its deputy leader to address the crowds but not its leader.

On the other side of the English Channel, the Europeans wait and wait. Donald Tusk, president of the European Council, told legislators Wednesday in Brussels that the E.U. should be open to a long extension if Britain wanted to “rethink” its strategy.

“You cannot betray the 6 million people who signed a petition to revoke Article 50 — the 1 million people who marched for a people’s vote or the increasing majority of people who want to remain in the European Union,” Tusk said.

Tusk was referring to the “Cancel Brexit” petition hosted on Parliament’s website, alongside the mass demonstration staged Saturday in London — probably the biggest public demonstration in Britain in a century.

a large clock tower towering over the city of london: British lawmakers are trying to sort out what sort of Brexit they want.© Adrian Dennis/AFP/Getty Images British lawmakers are trying to sort out what sort of Brexit they want.

The general division in the parliament gave no clear indication to the Europeans on the other side of the negotiating table what London might favor. Still, European leaders who gathered last week to give Britain a brief respite from its Brexit date also said they could extend the clock even further — if only the Brits would hold late-May elections for the European Parliament.

Thus far, May has refused.

E.U. leaders would also embrace a British move to stay in the European Customs Union. Although that possibility was among the rejected on Wednesday, it was still one of the more popular choices. Some negotiators have said that arrangements for Britain to stay in the customs union could be made within hours — not days or weeks — and it would ensure that the Irish border remains open. But Britain would be stuck without an independent trade policy, a disappointment to ardent Brexiteers.

Michael Birnbaum and Quentin Ariès in Brussels contributed to this report.

william.booth@washpost.com

karla.adam@washpost.com