Speaking as an engineering professional, with a considerable body of knowledge that bears on this problem and a kid to put through college: Don't hold your breath, pay me by the hour, and in advance.
You're trying to achieve something like a 99% CEP on a 10cm diameter target, from about 2500 meters away. That means that you have to aim the bullet to within 4 microradians, reliably. Just making a platform that can aim a rifle, be stable to within 4 microradians is not trivial. Add to that the fact that you probably want it to work when the ground is moving, when the wind is blowing, etc., after it's been exposed to sand and sea and shock, after its been fired hundreds of times, and over a temperature range from -40C to +55C, and just this one part of your robot sniper is going to set the DOD back by about $50 to $100K per.
Then, as others have mentioned, taking windage, sun loading on the rifle, and all the other effects into account, the problem becomes sheer magic.
You'll end up with a system that will cost a good chuck of $1M _in quantity_*, will require the services of several on-site repair technicians, not to mention a cadre of personnel back at the factory, will weigh something on the order of five hundred pounds, and will _still_ need one smart marksman to make it all work.
Contrast that cost with the resources needed to put one talented rancher's son on the line with a good rifle.
There is work being done on smart munitions of a size for anti-personnel use -- this probably makes a heck of a lot more sense than trying to make an automagic gun-firing machine. Sending out 100 Predators, each with a 500 pound smart bomb, is probably cheaper than fielding one sniper-bot.
- For _just_ a prototype I figure you'll be upwards of ten man-years of just engineering time, plus at least ten again of direct support personnel to the engineers, plus five more of management, program management, sales and other suits. And that's just on the side of the company designing the 'sniper robot'. The military would have to put at least another ten man-years into it, if not the same 25 that the company is, and that's just to get one frigging prototype -- complete with bugs severe enough to keep it out of Iraq -- on a firing range somewhere in Nevada so that a Colonel or a one-star general can say "why in hell can't we just train up a smart kid to do this?"