UK's embattled prime minister fights for her job amid mounting Brexit rebellion

LONDON -- Britain's embattled Prime Minister said she's fighting for her political life "with every fiber of my being" as dozens of Conservative MPs declared they have no confidence in her leadership.

Theresa May has been struggling to rally support behind her draft of an agreement plan for the U.K. to withdraw from the European Union since it was signed in Brussels on Tuesday and published online Wednesday night.

She took to the airwaves on Friday to directly address citizens' concerns in a 30-minute phone-in on LBC radio.

Responding to a caller who told her he was grateful for her service but asked her to stand down, she said: "You mentioned sovereignty was a really important issue for you, and you're absolutely right. For a lot of people who voted 'Leave,' what they wanted to do was to make sure that decisions on things like who could come into the country would be taken by us here in the U.K. and not by Brussels. That's exactly what the deal that I've negotiated delivers."

On Thursday morning, Brexit Secretary Dominic Raab resigned, saying he couldn't support the plan, with a second cabinet secretary resigning shortly thereafter, followed by two junior ministers and a parliamentary aide.

There are divisions between those who want the U.K. to cut most ties to the E.U., and those who campaigned to remain in the E.U. and now are advocating for a close relationship with the bloc for economic reasons.

Both sides have issues with May's plan with Brussels, which has been attacked as ceding too much control.

In 2016, 52 percent of the U.K. voted to leave the E.U. after a divisive referendum. The question on the ballot paper simply asked whether the U.K. should remain or leave, and the country remains bitterly divided on the details of what the new relationship with Brussels should look like.

On Thursday, May faced a grueling session in Parliament in which she took hostile questions for nearly three hours -- anger and criticism from all sides of the Commons, including bruising attacks from her own members of Parliament.

There were shouts of "Resign!" as she delivered her opening statement that argued the deal she'd negotiated was Britain's best offer from Brussels.

She later held a press conference at Downing Street and took questions from journalists, some of whom asked about the effectiveness of her leadership when her party appeared in open revolt.

"I believe with every fiber of my being that the course I have set out is the right one," she said. "From the very beginning, I have known what I wanted to deliver for the British people to honor their vote in the referendum."

"The British people," she added, "just want to get on with it -- they are looking to the Conservative party to deliver."

When asked by ABC News what she would say to Britain's friends and allies anxious about the current chaos, she said, "I think they see a government intent on working ... to ensure we can deliver a good deal for the British people."

At the same time, an influential Conservative MP exited the Commons and announced he had written a letter to the chairman of an influential party committee saying he had no confidence in the PM's leadership.

Jacob Rees-Mogg chairs an influential group of around 60 Conservative MPs called the European Research Group.

Speaking outside the Commons he told the press: "This is not Brexit. This is a failure of government policy. It needs to be rejected."

He added: "What we need is a leader who will say to the E.U. it is impossible to divide the U.K., it is impossible to agree to a situation where we have a perpetual customs union, it is impossible to pay 39 billion pounds of taxpayers' money for a few promises which was meant to be 39 billion pounds for the implementation of a deal, and it is impossible for us to allow the continued jurisdiction of the European Court of Justice. The problem is the negotiations have given away on all the key points."

There is a mechanism whereby a leadership challenge may be triggered should the 1922 committee receive letters of no confidence in the party leader from 15 percent of Conservative MPs. As the party has 317 MPs, 48 letters would be required.

It is unclear whether Graham Brady, the committee chairman, has received enough letters to cross that threshold.