I don't believe that the FF sensors cost dramatically more to make than 1.6 crop sensors.
I do believe that. Exponential error rates truly are a bitch. But although an aps-c sensor can be manufactured for a couple of dozens of dollars tops, an FF sensor doesn't need to cost more than a few hundred dollars. You'd think that a $700 Rebel with a FF sensor slapped on would fit the bill.
However, stuff like the shutter, the mirror mechanism and the pentaprism needs to be a lot bigger too, and that isn't exactly cheap either. Now you can save money on most of those (say: pentamirror instead of prism) but that would chip away at the quality of both camera and images. And quality is exactly the reason to choose FF over crop. It would make no sense to produce an extremely cheap FF camera, unless of course the market for gear whores becomes substantially bigger than that for actual photographers. I may be naive, but I don't think that's the case yet.
By the way: every few decades prices double because of inflation, so a sub-$1000-camera will be less likely every year. If it is to happen, it'll need to happen in the very near future - say less than five years. Unless Sony starts making 450mm sensor wafers with excellent yields real soon, and I don't see that happening. And I don't see Canon invest in that sort of tech anytime soon at all.
All in all, my guess is never, but you may get lucky between 2015 and 2020