To access the console you must remove the comment from the xstartup.cfg file normally located at: C:\Program Files\Entertainment\NBA Live 2003\main\cscripts\xstartup.cfg.
The original line reads:
//bind +K_TILDE CONSOLE
Your new line should read:
bind +K_TILDE CONSOLE
Making the above modifications will enable access to the console via the ~ (tilde) key.
I'm not sure what you can do from the console, but this will get you to it.