British Prime Minister Theresa May will face a vote of no-confidence from members of her own Conservative party on Wednesday. The threshold of support needed to trigger a no-confidence vote in the prime minister was reached Tuesday evening, according to Graham Brady, chairman of the Conservative Party's '1922 Committee', a group of influential backbench members of parliament (MPs). The vote was triggered after 15 percent of the Conservative parliamentary party submitted letters to Brady in recent weeks. A ballot will now be held between 1800 to 2000 (London time) on December 12, the 1922 Committee said in a press release. "I will contest that vote with everything I've got," Theresa May said on the steps of Downing Street on Wednesday. By mid-morning, 110 Conservative MPs had publicly backed the prime minister, Sky News reported. May needs a simple majority to win the confidence vote, that is, 158 out of the 315 Conservative MPs eligible to vote in the secret ballot. She said the entire Brexit process would be put at risk if a change of leadership took place. "The British people want us to get on with it (Brexit) and they want us to focus on the other matters that matter to them too."

The Chairman of the 1922 Committee Graham Brady told reporters outside the Houses of Parliament on Wednesday that he had spoken with the prime minister Tuesday evening after the confidence vote threshold was met. "It is beneficial to resolve this matter as quickly and as smoothly as possible," he told CNBC's Willem Marx. May has already received the backing of key ministers in her Cabinet, including from those seen as potential future Conservative leaders, such as Environment Secretary Michael Gove. Gove Tweet: Home Secretary Sajid Javid also voiced his support, saying the "country does not need a leadership election right now." Javid Tweet: Under party rules, if 48 Conservative MPs submit letters to the chair of the 1922 Committee stating they no longer support her, a confidence vote is held. One of the MPs that submitted a letter of no-confidence is prominent and influential Brexiteer Jacob Rees-Mogg. Although he was a one-time ally of Theresa May, he told CNBC on Tuesday that now it is May's "duty" to resign. "Normally when a prime minister loses her main policy she resigns, that is the main constitutional convention, they don't just carry on regardless … The prime minister only holds office as long as she maintains the confidence of the House of Commons (the lower house of the U.K.'s parliament)," he said, adding: "I think (on Monday when she announced the parliamentary vote would be delayed) the prime minister lost that and ought to resign."

If May loses the vote Wednesday evening, a leadership challenge would be announced (May would not be allowed to stand for re-election) and a general election would likely follow.

Backstop problems

The leadership vote comes as Theresa May desperately tries to salvage her Brexit deal after widespread opposition to the 'withdrawal agreement.' May went on the charm offensive on the continent Tuesday after pulling the plug on a parliamentary vote on the deal that was due on Tuesday. The deal had faced stiff opposition from many MPs from both the pro-Brexit and 'Remainer' camp in parliament, from those within her own Conservative party and other opposition parties. Her decision to delay the parliamentary vote – known as a "meaningful vote" on the deal and designed to give MPs a say on the withdrawal agreement – was made as it became clear that the Brexit deal, at least in its current form, would not be approved by a majority in parliament. For most MPs, the main bone of contention is what's known as the Northern Irish "backstop."