Depends on the game, both optimisation and technical requirements of the game itself. Running everything cranked to the right? Then you will want at least a 2080ti to stay around 4k/60 in most intensive current gen titles. Willing to sacrifice a couple of settings that don't make a large overall visual difference but hog a tonne of processing power? Then even a 1080ti will get reasonably stable 50-60fps at 4K while looking almost as good. Willing to crank some stuff even further down and impact the visuals noticeably but not catastrophically? (IE, it will still look better than a console most of the time and in the worst cases, on par) Then my old 980ti could handle 4K/60 with some work and tweaking.
But most people think of the first scenario when they ask questions like this and in that case, as I said, it's expensive and the new consoles won't be doing it at the price they need to sell them at. The hardware can and will run 4K/60 but it's not going to be comparable to a high end PC with everything cranked in a graphically intensive next-gen games. Which IMO, is perfectly fine, it doesn't need to be and games will still look stunning on next-gen consoles.
