Here's my reasoning fwiw - the chart below is from the yougov MRP poll (20,000 people responded so it should be reliable in it's findings). It's asking about May's deal, but I think the figures would be pretty similar for most other forms of negotiated soft brexit.
While the population is more or less 50/50 split over remain/leave, the leavers will support leave by whatever method: deal if that's what there is, or no deal if necessary.
A substantial number of remainers would go for the deal though, if it were a choice between deal or no deal.
The weak point is the remainers, a substantial number of whom will do whatever is necessary to avoid no deal - so in the end, that's the way the deadlock will break. Because no-one else is budging.