Theresa May promises to resign if MPs back her Brexit deal, but still no signs of consensus

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British Prime Minister Theresa May has promised to resign if Parliament backs her withdrawal agreement with the European Union, but that self-sacrifice doesn’t appear to have been enough to get the deal approved.

Ms. May has struggled for months to get the agreement through the House of Commons, only to see it rejected twice by wide margins. On Wednesday, members of Parliament took over the Brexit agenda and began trying to find a different way forward, but they found it just as difficult to reach a consensus, and failed to get a majority on any of the eight alternatives put forward, including revoking Brexit or holding another referendum. They plan to try again on Monday.

The Prime Minister has been stymied largely by a group of fellow Conservative Party MPs who bitterly oppose the withdrawal agreement and call her a weak negotiator. In a final bid to win them over, Ms. May said on Wednesday that if they backed the deal, she would quit and let someone else take over the next phase of the Brexit process, which would involve negotiating a trade deal with the EU. “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 told a meeting of the Tory caucus. “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.”

Her offer won over some opponents, including former foreign secretary Boris Johnson, who is a leading contender to replace Ms. May, and has been among her toughest critics. After the meeting, he said he would vote for the agreement. But several other Tories remained unconvinced. "I’m consumed with a ferocious rage after that pantomime,” Tory MP Steve Baker said after the caucus meeting. "I could tear this place down and bulldoze it into the river. These fools and knaves and cowards are voting on things they don’t even understand.”

In another blow to Ms. May, Northern Ireland’s Democratic Unionist Party, whose 10 MPs prop up her minority government, also remained opposed. The DUP has been particularly critical of a provision known as the backstop that is intended to ensure there is no hard Irish border by keeping Northern Ireland closer to EU regulations after Brexit. The party argues Northern Ireland would be cut off from the rest of the country, and DUP Leader Arlene Foster said on Wednesday that the deal "poses a threat to the integrity of the U.K.”

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Labour Leader Jeremy Corbyn said Ms. May’s offer to quit showed “once and for all that her chaotic Brexit negotiations have been about party management, not principles or the public interest.”

It’s not clear what Ms. May will do if the agreement is rejected for a third time or if she decides not to bring it back for another vote. In those circumstances, Ms. May would have to tell the EU before April 12 if she had another plan. If not, the country would either leave without a deal on April 12, or have to remain and participate in elections to the European Parliament that begin on May 23. In that case, Brexit would be delayed for months or years.

The party can’t force Ms. May out as its leader because she won a confidence vote among Tory MPs in December and her leadership can’t be contested again for a year. However, she will continue to come under intense pressure to resign, particularly since Mr. Johnson and other contenders have been lining up support. The party’s leadership process is fairly quick, and if she did resign, a new leader, who would also become prime minister, would be in place within about six weeks.

Parliament had been pushing for weeks to take over the Brexit process to find a way around Ms. May’s unpopular deal. But on Wednesday, it became all too clear MPs will have just as hard a time finding a solution.

In Wednesday’s unprecedented votes, MPs considered eight, non-binding Brexit options. They included remaining in the EU, negotiating a kind of common market with the bloc, leaving without a deal, holding another Brexit referendum and variations on a customs union. None won a majority, and the one that got the most votes was the option of holding another referendum, which was backed by 268 MPs and opposed by 295. The option that came closest to winning a majority was negotiating a customs union with the EU to ensure the free movement of goods. That lost by 264 votes to 272.

“It is of course a very great disappointment that the House [of Commons] has not chosen to find a majority for any proposition,” said Tory MP Oliver Letwin, who led the push for MPs to take over the Brexit agenda. “If on Monday the House is able to reach a majority view, I think that would be in the interests of our constituents.”

But the government said the votes only demonstrated that MPs should back Ms. May’s deal. “The House has today considered a wide variety of options as a way forward,” Brexit Secretary Stephen Barclay told Parliament. “And it demonstrates that there are no easy options here. There is no simple way forward. … The results of the process this House has gone through today strengthens our view that the deal the government has negotiated is the best option.”

The government is considering bringing Ms. May’s deal back for a vote on Friday, but that will happen only if it has a chance to pass. On Wednesday, Speaker of the House of Commons John Bercow reiterated his ruling that Ms. May cannot simply bring back the deal MPs have rejected. It must be changed substantially, he said.