On every Mac I've ever used, the key marked "delete", sitting to the right of = and above \, performs the backspace function. If yours is working differently, then something is misconfigured. Or your keyboard is defective. You need to figure that out rather than try to work around it by mapping a function key.
The most likely cause is your keyboard layout setting is incorrect. Go to System Preferences -> Language & Text -> Input Sources, select U.S., and make sure nothing else is selected. See if that changes anything. If not, try creating a new user account, and see if that account has the same problem.