You might be able to push 1080p in those games with a $1000 laptop, but you're going to have a real rough time. Is there any reason a desktop is unfeasible for you?
At best you're gonna see a 860m as a video card, and most laptops in that range have a weaker GPU than that. That's equivalent to a 650 Ti, a thoroughly midrange card that's almost 2 generations old.