The resignation of a key driver of the U.K.’s Brexit process is a blow for British Prime Minister Theresa May, but analysts believe she can survive the departure. Brexit Secretary David Davis resigned Sunday evening, objecting to May’s withdrawal plan that seeks to maintain close economic ties with the European Union (EU), rather than a harder separation favored by Davis and other so-called “Brexiteers.” Former Housing Minister Dominic Raab was named as Davis' successor on Monday morning. Analysts are seeing the latest move as a “crunch point” for May, but that the vagaries of British politics and need for leadership just nine months before the official Brexit date could mean that she can soldier on.

Brexit Secretary David Davis arriving in Downing Street, London, for a Cabinet meeting. Stefan Rousseau | PA Images | Getty Image

“I think what we’re seeing is the difficult choices over Brexit suddenly having to be confronted,” Ian Begg, a professorial research fellow at the LSE’s European Institute, told CNBC’s “Squawk Box Europe” Monday. “For the last six months, or even since the referendum, the can has been kicked down the road about making those hard choices between being in the single market or not being in it, in the customs union or not in the customs union. And when it comes to that, one side has to lose,” he said.

General election unlikely for now

Whether May can depend on the support of Brexiteers in her Cabinet and in her wider Conservative party is uncertain following Davis’ resignation. Brexit campaigners have praised Davis for sticking to his principles while the opposition has rounded on May, saying her leadership looks vulnerable. Jeremy Corbyn, the leader of the opposition Labour party, tweeted that Davis’ resignation showed May had no authority left. Tweet The First Minister of Scotland, Nicola Sturgeon, also said on Twitter Monday that “this U.K. government is in utter chaos and ebbing authority by the day.” Meanwhile Tom Brake, a member of the Liberal Democrats and the party’s Brexit spokesman said the latest move in the divisive Brexit process was akin to a “Tory psychodrama.” Tweet Analysts believe that May’s leadership is fragile but that a leadership challenge and possible general election was unlikely for now. “The underlying politics of this is that so many in the Conservative party are fed up with Mrs May’s approach, they’ve kept her in power because they don’t want to precipitate either a leadership election or general election, but this is a crunch point,” Begg said. “If the pro-Brexit members of her party say ‘we’re not having this’ they have the numbers to bring her down,” he added. The only thing that could prevent pro-Brexit politicians from trying to oust May would be that they could go on to lose their own seats in parliament should a general election be held.

Robin Bew, the managing director of the Economist Intelligence Unit, believes May could also withstand the latest shock, however. He tweeted several comments explaining why he didn’t believe David Davis’ resignation was a disaster for May. “Don't see David Davis resignation threatening May. That would require mass coordinated resignations. Not just addition of (Foreign Secretary Boris Johnson). Hard #Brexit camp could force leadership contest but can't win one. So what's the point? #UK Gov limps on,” he tweeted. May’s newly revealed Brexit policy has already brought damage to her cabinet, yet it’s unknown whether the EU would even accept the U.K.’s plans. David Henig, the director of independent think tank, the European Centre for International Political Economy, noted that the issue of whether the plan would even be accepted by the EU was uncertain. The LSE’s Begg agreed, telling CNBC it was unlikely that Brussels would even accept May’s plans. “From Brussels’ point of view, they’re going to push back because they’re uncomfortable with many of the things that were apparently agreed by the cabinet last Friday. They will see some of these proposals as ‘cherry-picking’,” Begg said.

A ‘reluctant conscript’

Stating he was not willing to be a “reluctant conscript” in the prime minister’s latest Brexit policy, Davis said it was increasingly unlikely that Britain would leave the European Union’s customs union — which allows for tariff-free trade within the 28-country bloc — and that the plan would not give Britain control over its laws and future trade relationships. Speaking Monday to the BBC, Davis said May’s policy for Brexit had a “number of weaknesses” and that he fears the EU will demand further concessions in Brexit talks. He hoped his resignation would put pressure on the U.K. government not to make those concessions. Davis said May would be able to survive his resignation and would not support a challenge to her leadership. Still, his departure and growing dissent among his fellow Brexiteers means that opposition politicians and political commentators are assessing the prime minister’s future. May appeared to secure a government agreement on the country's Brexit position last Friday with the Cabinet, made up of Remainers and Brexiteers, appearing to back her plan for a U.K.-EU free trade area for goods and agricultural products. She also said the plan for a new customs model would allow the U.K. to seek trade deals with the rest of the world. The deal was seen as a compromise and appeared to meet with reluctant approval from Brexiteers within May’s inner circle, the Cabinet. Cracks appeared over the weekend, however, with core Brexiteers mounting an opposition to the deal.