Britain’s Prime Minister Theresa May speaks in the House of Commons in London on Tuesday before lawmakers vote on the government's Brexit deal. Parliament strongly rejected the deal May had negotiated with the European Union and told her to come up with a new plan by Monday. (Mark Duffy/Agence France-Presse/Getty Images)

British Prime Minister Theresa May survived a vote in Parliament on Wednesday to push her out of office. But she faces a tough battle over her plan on how Britain will leave the European Union. Lawmakers on Tuesday demolished the divorce deal she had worked on for nearly two years.

British voters in 2016 supported the idea of leaving the European Union, a group of 28 countries that work together to make it easier for goods and people to move among those countries. Many thought Britain wasn’t getting enough benefits for the amount of money it was paying to be part of the group.

May says that Britain’s exit (or Brexit) deal means ending the free movement of workers to Britain from the E.U. and leaving the E.U.’s single market and customs union. (A customs union means the group agrees on how much to tax goods from other places.)

Many lawmakers think a softer departure that keeps the single market or customs union membership is the only plan capable of winning a majority in Parliament. They fear the alternative is an abrupt “no-deal” withdrawal from the group, which businesses fear would cause big problems at borders, ports and airports.

May has until Monday to present Parliament with a new plan. The prime minister called on opposition politicians in Parliament to “put self-interest aside” and find a consensus on Britain’s path out of the E.U.

But there’s a growing chance that Britain may seek to postpone its March 29 departure date while politicians work on changes — or even hand the decision back to voters in a new referendum on Britain’s E.U. membership.