British Prime Minister Theresa May is facing new challenges to her leadership the day after protesters packed the streets of London to demand a second referendum on Britain's exit from the European Union.

A number of British parliamentarians, including senior members of May's own Conservative Party, have wanted her out for some time, NPR's Frank Langfitt tells Weekend Edition Sunday. British newspapers on Sunday reported that senior members of May's cabinet could resign in order to force her resignation.

Parliament could also ask May to commit to a date to step down in exchange for an approval of her Brexit deal, though that seems unlikely given that her plan is so unpopular and has been soundly defeated in two votes.

May has not responded to the reports, but No. 10 Downing St. insists she is going nowhere. While many parliamentarians have lost faith in May to deliver on Brexit, senior members of her cabinet are dismissing reports that a cabinet coup is in the works.

"Changing the players doesn't solve the problem," Chancellor of the Exchequer Philip Hammond told Sky News on Sunday. "The problem is that we as a nation have to decide how to deliver Brexit."

Despite the pressure she is facing to step down, May has survived two no-confidence votes in Parliament, the most recent being in January of this year.

Still, May angered lawmakers last week when she delivered a speech blaming Parliament for the Brexit stalemate. And if Saturday's demonstrations are any indication, May is also losing support among voters. An Ipsos/MORI poll released this past week shows that 86 percent of Britons are dissatisfied with her leadership.

Protesters told Langfitt that they want a second chance to vote on Brexit because they believe the vote in 2016 was flawed.

"This country's in grave danger of shooting itself in the foot," Tim Parsons, who works in finance in London, told Langfitt. "There was a vote. Nobody knew what they were voting for at the time, so I think it should be put back for another vote. At least it will have been an informed decision."

The chances of a second referendum are considered low because it would enrage the 52 percent of voters who supported Brexit. Even some who voted to remain in the European Union feel a second vote would be anti-democratic, Langfitt says.

The leadership drama comes as May is running out of time to get a new Brexit deal approved by Parliament. She has until the end of next week to secure an agreement, after winning an extension from EU leaders. Britain was originally scheduled to leave the EU on March 29.

May could present her Brexit plan for a third vote next week, but she has said she would only do that if she was certain it had enough support to win. If Parliament can agree on a plan next week, the United Kingdom will have until May 22 to leave the EU. But if Parliament can't get a deal done, it will have to devise a new plan or leave the EU with a "no-deal" Brexit on April 12, which most experts say would be a nightmare scenario.

Copyright 2019 NPR. To see more, visit https://www.npr.org.