Yes and No, and let me explain both:
No. Bitcoins circulation is not large enough to power an entire country let alone the world. It can become a de facto standard of moving wealth/value, but will remain so as a fatherless/motherless currency (at best).
Bitcoin has its fair share of problem (confirmation takes too much time, the 51% forking issue remains, number of transactions per second is limited, block size issues, etc.)
It will most likely not die. It will definitely become an important currency to allow cross-border trade amongst various facets of business society, from free-lancers getting paid, to cross-border remittance rails.
However, it will not be the final straw or the final currency that we will see.
Yes. Bitcoin opened avenues on how peer-to-peer value exchange can be done (using the blockchain).
But all these are problems Bitcoin Version 2.0 could solve and be adopted. Who knows the next variant of LiteCoin or Dash or Ethereums Ethers could be exactly what we are looking at. The concept of Bitcoin gets my Yes vote for the future of money. Governments will realize the power (and benefits) of digital money - some already are, but cash and other paper instruments still remain. At some point in time governments might just issue their own version of the bitcoin enabling transactions without the need of intermediaries
I disagree on the point of Bitcoin not being large enough to power an entire country (economy)
It may be not scalable enough to power an entire country (though even that is debatable), but in terms of size (since that's your point and don't try to sidestep it), it is already quite on par with half the world. I refer not to the actual half of the world as such, of course, but to countries which this world consists of. Someone has already posted a list of countries with the size of their economies (more specifically, amount of money in circulation, in dollar terms) and Bitcoin would be somewhere in the middle of this list given its current market cap. Therefore, if it weren't for scalability issues, Bitcoin could easily power on a mid-sized country like Greece or Bulgaria