Long story short? Nothing. The economy can be ran off any quantity of currency as long as the market value of the currency is allowed to float to meet the market demand.
Discussion
As long as the currency is divisible and the value of the currency is allowed to grow to meet the amount of trade done then we could operate the whole economy on just a few bitcoin. This could look like a market cap in the quadrillions or more (depending how few bitcoin were in circulation) but if that occurred it would incentivise people and nation states to use some of their bitcoin which would add more float into the market. (decreasing the purchasing power of the bitcoin in circulation) this would theoretically occur until an imbalance came about where the perceived value of holding was higher than the percieved value of spending and the cycle would repeat. hope that helps elucidate my thought process.