The no confidence vote will fail because there's not a single Tory or DUP MP who will support it. May will, nominally, consult with the other party leaders, but has clearly set out that she won't support a customs union, which is the minimum that Labour would accept to support her (they'd expect some additional workers' protections too, but those could be finessed). So on Monday she'll return to parliament with a deal that's virtually identical to yesterday's and it'll be comprehensively rejected again.
At that point, she'll propose an extension to Article 50 and the EU will accept. May will probably start to pursue a Norway+ model, pressured by Labour to go for a harder customs union. The EU *might* soften their position a bit, recognising that all the above makes a hard Brexit a genuine possibility.
I am increasingly convinced that the Labour shadow cabinet won't support a second referendum under any circumstances. It's just possible that an extension to Article 50 and the intransigence of the Tory & Labour executives will precipitate the formation of a new, centrist pro-Remain party, but I wouldn't be betting my last tenner on it.
EDITED: 16 Jan 2019 07:07 by MANTHORP