British prime minister Theresa May will face a vote of no confidence from her Tory Party over opposition to the Brexit deal she agreed to with the E.U.

Most of the opposition in her own party to the Brexit deal is coming from members who believe that the deal doesn't go far enough and is disadvantageous to Great Britain.  There are also complaints about the Northern Ireland "backstop" she negotiated, which solves little and has angered some Northern Irish members of her coalition.

That said, May has several powerful arguments to make that could forestall her exit.

Politico:

The news came after May delayed a House of Commons vote on her Brexit deal, which had been due to take place Tuesday night. Instead, she spent Tuesday touring European capitals in a bid to secure assurances over the controversial Northern Irish backstop from other EU27 leaders in the hope of winning over more Tory MPs, many of whom have said they opposed the divorce deal the prime minister negotiated with Brussels.

Speaking outside No.10 Downing Street, May warned a change of leadership now would "create uncertainty when we can least afford it" and said any new prime minister would be forced to extend the Article 50 Brexit negotiating period or revoke it all together.

A contest could not be completed before the January 21 deadline she has set for a parliamentary vote on her Brexit deal, she said, warning that a leadership contest "risks handing control to opposition MPs in parliament."

Arguing that a leadership change would not change the parliamentary arithmetic, she said the "only people" who would benefit were Labour leader Jeremy Corbyn and his Shadow Chancellor John McDonnell.

How much trouble is May really in?  There is the "hard Brexit" faction headed by her former foreign secretary Boris Johnson.  But how much support he has will depend on how many Tories truly want a "no Brexit" deal.  The E.U. has set a firm date for Great Britain's exit – March 29 of next year.  If no deal is in place, there will be confusion and chaos up and down the European economies, as trade would come to a standstill, and perhaps even financial transactions would be severely affected.  A change in leadership – presumably to renegotiate a deal – would mean that there wouldn't be an agreement in time.

May's Brexit deal is just about as good as anyone could expect.  It doesn't satisfy the hardliners, but they and their Tory colleagues will now be faced with the reality of a date certain for British exit from the E.U.  It's safe to say that if the hard Brexit faction blows up the deal by sidelining May, there will be early elections that would not go well for the Tories.

In the end, realism may very well trump ideology on Brexit and May could hang on.  But there is huge uncertainty as to what will happen when Great Britain leaves the E.U., even with May's flawed deal.  That uncertainty may also work in the prime minister's favor.