EDIT: 4000 tps and even 45000 tps theoretically but considering how many we have in the fiat world now despite all its inefficiencies we could easily be looking at 4 billion tps at some stage.
Obviously the technique can be improved a LOT before we would be hitting limits anywhere even remotely near that. And computers that far in the future will also be a lot more powerful.
Bitcoin will fail because involved people are lost in the future, instead of focusing on the present.
edit: Quod Erat Demonstrandum >
http://www.reddit.com/r/relationships/comments/2uovrl/me_28_f_with_my_husband_31_m_5_years_will_not/ "I used to consider him a smart guy and I never, ever thought he would succomb to basically being brainwashed by a bunch of clueless idiots on the internet who seem to know absolutely nothing about finance or the real world."