Bitcoin can currently handle about 2 transactions per second.
First, this isn't the real number and second 'handle' doesn't describe the situation, which is an artificial limitation built in as an artifact. Whether you are in the camp that believes this will be worked around in bitcoin or not is irrelevant, on a technical level any cryptocurrency can be created that can handle MANY more transactions.
Right now you could sync to the blockchain on the bandwidth T-Mobile gives for free while on international roam in 100 countries.
So the amount of data handled by every node is not even close to any sort of practical limit. Anyone with Netflix could sync to 50x the number of transactions.
That isn't the problem with things like this. The problem is trust, transparency and accountability. The old "A rasberry PI could handle the same amount of transactions" misses the point completely.
This is a particularly gross distortion of reality by people who for whatever reason want people to believe cryptographic currencies won't scale.
In the infancy of a currency, when there aren't many transactions, the mining power amortized over each transaction will be much more than when many transactions are happening. Each transaction doesn't take mining power, the number of transactions and mining are completely decoupled.