Analysts at BBH suggest that many see UK Prime Minister May's speech at the end of the week as key, but they are skeptical.  

Key Quotes

“The government's position has crystallized:  leave the single market and customs union but strike a close trade deal with aligned regulations.  But it is DOA (dead-on-arrival).  Brussels has already rejected this approach, which strikes many of its officials as a cherry-picking exercise.”

“Perhaps more important for the evolution of Brexit is Labour leader Corbyn's speech at the start of the week.  Corbyn is likely to confirm a subtle shift in Labour's position to remaining in the customs union.   It may not sound like a significant move, but it sets the stage for parliament to possibly reject the Brexit deal the government negotiates.”

“Meanwhile, Remainers from both main parties is supporting an amendment to a trade bill along these lines.  The employer's association, CBI, also backs remaining in the customs union.  It also would solve the problem of the Irish border.  However, May's position is not untenable.  She could make the vote on the trade bill a vote of confidence.  In any event, a defeat for the Tories in local elections this spring could see a leadership challenge.”