When (not "if") Labour puts a motion of no confidence, it will all be down to the UDP. If they abstain the motion should pass. And with Theresa May still intent on her deal, with the non-exit backstop, the DUP can be expected to abstain.

And there is no prospect of the EU (especially Ireland) giving way on that part of the backstop.

Stuff about the EU being unreasonable in negotiating doesn't stand up to examination. It's the reverse, if anything, far more flexible than the UK. A year ago the UK essentially agreed to the backstop, to continue until and unless some alternative could be cobbled together to provide a permanent guarantee against a hard border, and did so specially in order to allow other negotiations to proceed - then after going ahead with those negotiations it has tried to backslide on it.

The £39 billion isn't a charge for an agreed withdrawal which can be dispensed with in a no deal exit, it's a debt which we'd be duty bound to pay however we leave. If the UK defaulted on that debt it would be acting illegally, and would do enormous damage to it's reputation. Financially it would be a rogue state, and no one would be likely to trust it. The old label "Perfidious Albion" would be revived, and justly so. And this would be a country hoping to set up favourable trade agreements round the world?