In his first visit to Britain, Donald Trump made quite the splash. In an interview with the British newspaper the Sun, Trump criticized British Prime Minister Theresa May, suggesting that her Brexit approach would “probably kill” any trade deal between Britain and the United States. “I actually told Theresa May how to do it, but she didn’t listen to me,” he said. The next day, he backtracked, insisting that the relationship between the two countries remained “the highest level of special.”

Trump’s visit came after a chaotic week in British politics. A few days earlier, two prominent Cabinet ministers resigned over the government’s approach to Brexit: Foreign Secretary Boris Johnson, one of Brexit’s most influential advocates, and Brexit Secretary David Davis. Four junior members of the government also quit, along with two vice chairs of the Conservative Party.

What’s happening in British politics — and what does all this mean for the Brexit negotiations?

The Conservative Party is divided over Brexit

The resignations came after May announced a new Brexit strategy, called a “soft Brexit,” that would keep Britain closely aligned to rules set by the European Union. Under the government’s plan, Britain would remain in the E.U.’s single market for goods, allowing British manufacturing and agricultural companies to continue trading freely with Europe. What’s more, this approach would help the British government avoid reimposing controls on the border between Northern Ireland and the Republic of Ireland — helping preserve the peace treaty that formally ended the conflict there in 1998. Britain would also have to accept future E.U. regulations. Services, meanwhile, such as finance and law, which make up some 80 percent of the British economy, would receive less access to the E.U. market. The European Court of Justice would probably play a role in settling disputes.

Johnson and other “hard Brexiteers” want a sharper break with the E.U. They view May’s approach as an unacceptable betrayal of British sovereignty — because after Brexit, Britain would remain subject to E.U. laws with no say in their creation.

In his resignation letter, Johnson wrote that the Brexit “dream is dying, suffocated by needless self-doubt,” and that Britain was “truly headed for the status of a colony.” Jacob Rees-Mogg, a leading pro-Brexit Conservative MP, colorfully described May’s plan as the “greatest vassalage since King John paid homage to Philip II at Le Goulet in 1200.” Obeying E.U. laws, they pointed out — much as Trump did — will also make it harder for Britain to strike external trade deals. If Britain has to abide by European rules on agricultural goods, for example, it will struggle to reach a comprehensive deal with the United States — the United States will probably want Britain to accept some U.S. products, such as certain genetically modified crops, that violate E.U. regulations.

These objections may be moot, as European leaders are unlikely to accept May’s proposal. She wants access to the single market for goods while insisting that unrestricted immigration must end. But the E.U. regards the “four freedoms” of the single market — the free movement of goods, services, capital and, crucially, people — as “indivisible,” meaning that Britain cannot choose one without accepting the rest.

According to one senior E.U. official, “it is not a question of whether we say ‘No’ to these proposals, but when and how we do it.”

What happens next?

Trump’s visit has heightened tensions within the Conservative Party. In a recently leaked recording, Johnson imagined Trump negotiating Brexit. “He’d go in bloody hard,” Johnson said. “There’d be all sorts of chaos. . . . But actually you might get somewhere.” In his interview with the Sun, Trump, in turn, said that Johnson “would make a great prime minister.” That may not help Johnson: In a recent poll, 77 percent of Britons said they had an unfavorable opinion of Trump, and there were large protests throughout his visit.

For now, Conservative hard-liners will struggle to topple May. Triggering a leadership election within the Conservative Party requires 48 MPs — 15 percent of the party’s representatives — to call for a no-confidence vote. That may be doable: The European Research Group, a pro-Brexit group of Conservative MPs, has roughly 70 members. But to win the vote, they need a majority of the party, at least 159 MPs, which would be a heavy lift. No leader waits in the wings who could unify the party. The Euroskeptic rebels are split among several contenders. Most Conservatives are wary of causing turmoil that could upset the party’s agreement with the Democratic Unionist Party, a small right-wing Northern Irish party the Conservatives depend on for support. That could trigger new elections, which they might well lose.

While May looks set to survive this crisis, it may not be long until the next one. The E.U. holds its next summit in October. May hopes to use it to sign a final deal on Brexit, which would then need Parliament’s approval. Because May has only a narrow majority, a few Conservative rebels can block any deal they don’t like.

What’s more, Labour MPs are unlikely to back a Conservative plan if they see an opportunity to topple the government. (Labour’s own policy on Brexit remains unclear.) If May loses a vote on whatever deal she eventually reaches, and the E.U. refuses to restart negotiations, the result could be new elections, Brexit without any negotiated settlement or even a second referendum. With or without a deal, Britain is due to leave the E.U. at 11 p.m. on March 29, 2019; if there’s no deal, it would become just another outsider nation, working with the E.U. on terms that would be little different from those that apply, say, to the United States or China.

For all the fireworks, Trump’s visit does not change the dynamics that make Brexit so challenging. May has to craft a deal that honors a referendum result she campaigned against; that unites a Conservative Party long fractured over Britain’s relationship with Europe; that minimizes the economic damage of Brexit; and that’s acceptable to a supermajority of the other 27 countries of the E.U. And she must do all this with a razor-thin parliamentary majority — and only eight months left.

Sam Winter-Levy is a PhD student in politics at Princeton University.

Alasdair Phillips-Robins is a staff editor at Foreign Affairs.