shoestring budget?

I know what “shoestring budget” and “shoestring operation” mean, but why a shoestring?

Anyone?

Anyone?

Bueller?

Because it is skinny, lasts a long time and everyone has one.

Seriously, does anyone have access to an OED? The answer might be there.

I did find this, but it’s not much more informative than The Devil’s Grandmother’s guess.