The Washington Post has a great article on the history of the debt ceiling (thanks Jun Ong for pointing me to it!)
Here is the upshot: Since Congress had to approve all debt issues, it thought it might be easier not to micromanage the Treasury during WWI, but simply provide a debt ceiling. The ceiling was not used as a bargaining chip until the mid 1950s, and the current president admits to having voted against the debt ceiling (during his time as a senator) for political reasons – which he now regrets 🙂
