While the answer I give on this occasion is the same as others have given (= try Microchip PIC 10F200) the ease of getting a reasonably good answer out suggests that you are not aware of it so it's worth noting. ie use any large suppliers online priced selector guide - in a competitive market they are as good as you'll be easily able to get at 1000 quantity except for specials
So, go to eg Digikey's website and key in microcontroller, select the largest volume option = emebedded microcontrollers = 33613 candidates, select sort by price (arrow above unit price for Digikey), key in "in stock" and 1000 quantity and select "Sort by price, advanced". Bingo.
PIC10F200T-I/OTCT-ND 34 cents US from 100 up!
As a check, take the lower priced candidates and plug them into eg Findchips . For the PIC10F200, 34 cents is as low as anyone advertsies on the open market via Findchips. You can bypass the front end with desired using eg http://www.findchips.com/avail?part=PIC10f200
If you want rather more than 1000 then people like Microchip have special untested supply lines where you are responsible for ensuring devices are in spec and you get accordingly low prices. These are sold in egh Asia to compete against the Asian direct PIC clones and against similar capability processors. Prices down to around 20 cents should be "easy enough" to get.
As you get to high volumes pricing becomes subject to NDA. I have seen prices of some products (not processors) which are around 25% of what may be reasonably expected at very high volumes. (No I'm not subject to NDA but also am not going to be more specific, alas). So, a 20c price in ongoing volume seems doable.