(CNN) UK Prime Minister Theresa May will be hoping the third time's the charm when she tries to get the House of Commons to back her Brexit deal this week after two previous defeats -- but she'll need more than just luck to get lawmakers to change their minds.

The question being posed in Downing Street this week is: What will it take for more than 70 lawmakers to back her and get her deal over the line? And does that plea bargain include the Prime Minister promising to step aside within weeks in return for more votes from her own Conservative side?

This suggestion is gaining ground in Westminster. On BBC radio yesterday, former Cabinet minister Esther McVey called on May to announce a "dignified departure" from No. 10 and to make way for a new Prime Minister whom, she argued, would be more enthusiastic about the UK making a clean break from the European Union. This view is shared by an increasing number of Conservative MPs (members of Parliament).

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McVey resigned from May's Cabinet last autumn in the wake of the Prime Minister agreeing her deal with Brussels. McVey says that withdrawal agreement is still a "bad deal" but that she has decided to vote for it when it returns to the Commons for a third time because she fears that otherwise Brexit may not happen at all.

McVey isn't the only Tory lawmaker who has switched sides and is planning to back the deal in the Commons. Several MPs have announced that they've changed their minds in recent days. Their number is not yet at 75 -- the figure May needs for victory -- but it is a significant start.

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