A single bitcoin can be split infinitely -- it's just a matter of adjusting the number of decimal points. Currently, a satoshi amounts to a millionth of a Bitcoin. If a Satoshi becomes more valuable, there may be more decimal points added.
Plus, they're already "split up" as it were, it's just they're not valuable enough that people are using nanobitcoins or anything like that. It's only when the value of the currency goes up that people will do transactions in smaller fractions of a bitcoin.
One satoshi is one hundred-millionth of a bitcoin, not a millionth of a bitcoin.