I appreciate your comment but they didn't just pluck the figure out of the air. The broke down in detail the costs in detail as they showed me around the underside, including probably 8 hours to take apart the transmission and the cost of the components that would need to be replaced, which are far from cheap in that part of a Prius. They also showed me various parts on the underside of the car that were badly damaged.
I should also have mentioned that the car has a lot of miles on it: 210k. I realise now that it was probably used as a taxi at some point and has been treated pretty badly throughout its life. I strongly believe the mechanics were not BS'ing me. On the other hand, the sales people clearly are motivated by making a sale on the best possible terms they can and want to get it done today. I'm not stupid. I'm just saying that I am in an very difficult situation because it is not just BS that the car might be worth next to nothing if it stops working completely in a few days.