I don't think responding in time is the problem, it's more the thought process in each hand. You have to be very very experienced and know exactly what to do in just about any situation that comes at you without thinking about it.
I can 4-table fine now, but even 6 is a little too much for me. fyi, 12 is nothing - people can apparently play up to like 40 tables. There's a youtube vid of someone doing 24, but I've heard of a lot more at once.