You are describing fractional reserve banking, which can be done with anything in theory. But there is no Bitcoin press in case of a run on the banks.
It can be done with full reserves. I lend 1 BTC, you lend 1 BTC, then they lend 1 BTC. Now there is 3 BTC worth of debt on real goods, and 1 BTC to pay them. Default is inevitable.
