This is highly unlikely.  It has significant potential for becoming A mainstream payment system, but it would require some significant changes to ever be versatile enough to become the single most significant payment system.

At the moment, due to the maximum size the protocol allows a block to be, bitcoin can handle approximately 7 transactions per second.  There is already significant debate about whether this limitation should be changed and how much larger it should be.  Such changes to the protocol require a consensus not only of miners but of all peers.  Given the significant spectrum of ideologies in bitcoin, such a consensus is extremely difficult to accomplish.

It is likely that either there will be multiple independent payment systems, of which bitcoin may be one, or that there will be payment systems that are backed by bitcoin.