Hard to say. 2 maybe 3 years perhaps at the rate we're going? Looking at the price of the still current 5DII and comparing that to the 6D I would think we're probably heading in that direction. A $1000 6D would probably sell to a lot of folks who would currently not considering upgrading their Rebels and 60Ds and stuff - and without added production cost really.
It's still too early but I see sensor size becoming the next marketing slogan for the market segment that is still looking at megapixels and ISO numbers.
The question is if there will be any actually usable mirrorless camera first or if it's a small(ish) SLR.
For around a 1000 bucks the 6D would make a really nice entry level camera or a decent backup camera for more invested folks. For 2K I don't see it making any sense in any market segment.
It's doubtfull that the 6d would make any kind of profit selling at or near 1K now. On paper it's very close to the 5d2, which after all this time still holds it's own in the market (retailing even now at $1800 new despite the fact that it is several years old now). Now, take the specs of the original 5d and put that in a small plastic body (rebel), make it SD card onlyand then you've potentially got a FF body at or around 1k. But, I really doubt that will happen as long as APS-C sensors are selling like hotcakes. And for the most part, those buying a sub $1000 body are either beginners (people who know a little bit about what the difference in crop vs FF is, but don't have the cash to justify spending a ton yet), casual users (who have no clue what the sensor even does, much less the size), ambitious P&S users upgrading (again, they most likely won't know the difference). So, until APS-C is phased out and everything is FF, I just don't see a 'new' FF body being available for 1K.
Oh, another way they could reduce costs is to run FF sensor lines that don't have as much quality control! Who wants that though?

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Do you folks have any sources for this talk about $1000 sensors?
Please explain to me how the 6D is $2100 and the D600 is at $2000 when the sensor alone is half of that price? I believe the 6D will be selling at $1700 in a matter of months. I've read that FF sensors cost $500 to manufacture a couple years ago, but I have never heard of them being $1000 to make.
For one --- Nikon is reaping the benefits from outsourcing their sensors to sony. Take all that R&D out of the equation and yeah, your cost to produce goes down. Another very valid point regarding nikons recent pricing --- they are making moves to gain market share - which means they very well may be making the trade off of less profit margin per body sold for quantity of bodies sold. Also, to correct ya, actual price of the d600 is $2100, it has a $100 rebate now which brings it down to $2000. Also, looking at the top sellers list from amazon --- it does really look like nikon made the d600 too nice! It does appear to be eating away at d800 sales! (the d800 had been in the top 20 since release, but, since the d600 came out it has slipped further and further back, down to 26th). The 6d is much less likely to eat away at mk3 sales, in fact, it may even sway people towards the mk3!
Will the price of all of these go down after release? Of course they will. But, it won't happen until the R&D/production costs are paid off. Retooling assembly lines to make new parts, all the time put into creating the tech -- once all that is paid off then the price can naturally go down. We keep throwing around #'s though like we're in canon's accounting dept, so I'll pretend too. Lets say for the first year (or make it more of a financial goal as opposed to time based. 6D, current cost to produce might actually be as high as $1500 (with all the added R&D, retooling costs, advertising, etc, etc). Lets say they need to sell 3 million of these at that price to pay off the production costs. Now we're left with actual cost to produce, which may be around 1k. It's probably not as cut and dry as that, there are other factors too. But I'd guess that this isn't too far off the case.
All that said - the mk3 the price will go down to around 3k around a year after release (this spring). Then the 6d will go down a bit by next november/december. And, by that time we'll have the new 7d to contend with and possibly a big MP body too, plus a slew of rebel updates. My guess is that we may see a natural price of $2700ish on the mk3 in 2014 , and the 6d may be down to around $1800 by then (the mk3 has more room to drop, I don't think we'll see the 6d go down to $1500 until it's closer to 6d2 time (a big q with that is product cycle. Most of the pro gear is on a 3 year cycle, but lower grade stuff is yearly. So how entry level is the 6d? Might next year bring a 6d2?)