I expect them to not even come close to 4k with most PS4 games.
Lets see what graphics card the ps3 has: The Nvidia RSX based on the Geforce 7800 GTX, but with 550 mhz. This graphics card in a pc could not play the latest games, like Skyrim or CoD 3, not now or then in 1080p. When it came out, games like Far Cry 1 and Doom 3 were the latest games. So how did they managed the 1080p resolution they pushed with the PS3? The PS3 has the Cell processor. A very powerful cpu for its time, but really complicated. But this combination of cpu and gpu works till today and let the latest games run very good on the PS3.
But as I said before, in most games they had to lower the resolution or to trim the graphics in another way. I think we will see the same with the PS4, if they won't upgrade the hardware extremely.
It is also not easy to compare pc specs to a console. We know that the hardware of the PS3 and Xbox 360 are ancient, but they still manage to run new games very good. They just don't have the problems a pc have. The games can be optimized to one hardware combination and not to nearly an unlimited amount on combinations on pc. The os is very small and doesnt need much ressources and no useless services are running under the hood like on a pc. Simple and powerful.
The AMD 6870 is a graphic card that you can buy for 150 , that
can display games in 3k resolution (5760x1080) with ease back in 2010. So why shouldnt a gpu based on a good current amd card with a good processor (next cell or a normal one) display 4k games?
They have a big advantage now, because the technology is already matured. Back in 2005/2006 it was the starting point of quad core cpus and such technologies. There are working clever people in the hardware apartments. Just think about how the smartphones have improved in the past years, it is getting crazy.
I cant wait till the next gen consoles. And while waiting for them, I just enjoy the games like GT5, Forza and others.